Structural Family Therapy for Multi-Stressed Families with Substance Abuse and Grandparents Raising Grandchildren

Structural Family Therapy

 

What is a family?

 

  • Extended families – they include grandparents, uncles, aunts, cousins etc.

Challenges of Grandparents raising grandchildren

 

  • Financial inadequacies – limited financial resources which make it difficult grandparents to cater for the needs of their grandchildren. Often, they have limited sources of income and rely on pension and savings from their youth. This is inadequate to provide for food, shelter, housing, and clothing for their grandchildren.
  • Physical Health – because of age, grandparents have limited energy and health problems that make it strenuous to raise multi-stressed children, which is physically exhausting.
  • Mental Health – Grandparents also suffer from mental health because of age related issues compared to the general population.
  •  Time – Tasked with the duty of raising grandchildren, grandparents have less time for themselves and for relaxing. This further makes them stressed and filled with anger and grief.

Family Therapy Models

The Family Systems Model – this model is founded on the belief families tend to arrange themselves around interactions substance abuse. This method focuses on how to build healthier organizational patterns in a family unit. For example, if a member of the family is encouraged to continue abusing drugs because it makes them more productive, then therapy is directed towards ensuring the family is corrected of this maladaptive behavior.

The family disease model – This model is based on the concept that addiction is a disease that affects the whole family. Family members that aren’t abusers may develop co-dependence, which will, in turn, cause them to enable the addict. This approach is geared towards modification of behavior and environment.

 

Cognitive Behavioral Family Therapy – this approach focuses on how to improve family relationships and to promote sobriety by correcting the disruptive behavior that leads to addiction. Family members are taught how to identify triggers of the substance abuser and how to handle these triggers.

Postmodern approaches – postmodern approaches are based on constructivist and social constructionist views on the subjective experience of reality. Moreover, therapeutic objectives are influenced by both family and therapist beliefs about healthy functioning (Walsh, 2012).

 

Benefits of family therapy for Substance Abuse

  • Improving communication – family therapy will aid in better communication especially in cases where there isn’t communication.
  • Awareness – Family therapy in substance abuse treatment helps families become aware of their own needs. A clearer understanding of the addiction and how it affects behavior – this is done via education from a therapist.
  • Setting boundaries – setting boundaries is an important aspect towards health recovery. In extreme instances, this may include detaching from a member who is a substance abuser.
  • Trust – members with substance abuse are usually dishonest because of shame and financial implications. With improved communication, honest interaction and positive change, members of a family gain trust.

substance abuse.

  • Cost benefit – The cost for family therapy can be economical and social. It is cheaper for a family to get a therapist for a family is cheaper that treatment costs for substance abuse. Family therapy also helps in preventative measures i.e. helps members of a family not get stringed along into substance abuse, which will then lead to cost saving.

Impact of substance abuse on families

 

  • Negativity – communication between family members, is usually critical and filled with anger and displeasure. The mood of the household is generally low, and communication is achieved by bringing up a crisis.
  • Anger – member that suffer from substance abuse have built up anger and most often, they express this anger to the wrong person. Communication with such individuals become difficult.
  • Inconsistency – parents that suffer from substance abuse usually set unrealistic rules that govern their household. Substance abusing parents often do not follow these rules and end up bringing up inconsistencies.

Approaches to family therapy in substance abuse

 

Impact of grandparents raising children is substance abuse

 

– most grandparents have small houses that have limited space for the upbringing of children. Children of different ages and gender are forced to share rooms, beds and sleeping material.  Grandchildren raised by grandparents are at a higher risk of bullying at school. This has the potential of impacting negatively on the child’s education and emotional stability. Most of the grandparents taking care of children are also highly involved with supporting the substance abuser. This impacts on the wider family, children also feel neglected, unwanted and build up feelings of resent towards their parents. Substance abuse and domestic violence also go hand in hand. This further alienates the children from their parents. These factors tend to impact negatively on the upbringing of a child. Grandparents  point out that they save the country a lot of money by taking in their grandchildren because if they didn’t, the children would become the problem of the state. They, therefore, request the government to aid in their financial situation by subsidies and support services. Grandchildren   of substance abuse are at a higher risk to drug and alcohol use, and when not yet present, grandparents have reported worries over the potential for future use.

Raising growing children leads to heightened physical and emotional demands. Grandparents often suffer from health issues related to age and are unable to cope with the situation. Familial drug abuse also poses risks to health, e.g., blood borne viruses and violence, and this is particularly problematic when grandparents are disabled or raising a disabled child.

Although grandparents raising children to deal with negative impacts, grandparents report a sense of pride in bringing up their grandchildren.  The build relationships with the children and further connect emotionally and feel very proud when the children excel in their lives and studies. On     the positive side, grandparents have had experience raising children, therefore, they know how to handle their grandchildren. This helps them understand complex situations and know how to manage the said situations without getting out of hand. Grandparents       can join support groups where they meet with other grandparents with similar circumstances. The support group meetings are confidential and help the grandparents on how to cope with multi-stressed children. Sharing issues helps one learn from other people’s experiences which in turn helps in making better decisions while raising multi-stressed families. There are also groups for children whose parents are substance abusers. This helps the children interact with other children that are going through the same situation. This makes the children know that they are not alone. The Children of Alcoholics Foundation (COAF) also has resources online that can help grandparents with raising children whose parents are addicted.

Conclusion

This paper provides an overview of how structural

References

Mensah, E., & Andreadi, H. (2016). Multi-family Group Therapy. Clinical Practice at the Edge of Care,175-196. Doi:10.1007/978-3-319-43570-1_9

Reiter, M. D. (2016). A Quick Guide to Case Conceptualization in Structural Family Therapy. Journal of Systemic Therapies, 35(2), 25-37. doi:10.1521/jsyt.2016.35.2.25

Sprang. G., Choi, M., Eslinger, J., & Whitt-Woosley, A. (2014). Grandparents as Parents: Investigating the Health and Well-Being of Trauma-Exposed Families, Lexington, KY: University of Kentucky Center on Trauma and Children.

Walsh, F. (n.d.). Family Therapy Systemic Approaches to Practice. Essentials of Clinical Social Work,160-185. doi:10.4135/9781483398266.n7

 

 

 

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Risks in Common Stock Investments

Risks in Common Stock Investment

According to the article, it is important to understand the risks that are involved whenever one wants to engage in stock investment. The article provides an insight of some of the risks and how one can easily measure their impacts on the investment at large. As far as risks in stock investment are concerned, the decision to take part in such investments would be determined by various factors. For instance, just as the article mentions, the profitability of the invested enterprise, price safety margin, as well as the stability of the financial status of the company in hand, are among the determinants of a successful common stock investment (Otuteye & Siddiquee, 2017).

For a common stock investor, the major risks that underlie usually surround the invested money and the returns. One of the major risks is that there is no guarantee that the investment might yield some good return (Otuteye & Siddiquee, 2017). It is a challenging process to determine if a stock investment would have a good performance, but one can assess the investment in various ways. However, the fact that it is not a guarantee for the stick prices to go up makes it a risk for the entire investment.

The investment in common stock is also associated with the fluctuation of stock prices, which might make the investor lose their money. This mostly happens when the investor opts to make a short term investment. Some of the reasons behind the loss of an investor’s money is the choice to buy on margin, among others.

When engaging in common stock in investment, what comes into a trader’s mind is the aspect of volatility. This entails the tendency of the price of stock to change fast and by a large degree (Otuteye & Siddiquee, 2017). Thus, using beta and standard deviation as ways to measure volatility, a trader would be in a better position to determine the risks that are associated with such an investment.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

References

Otuteye, E., & Siddiquee, M. (2017). Re-Evaluating the Value of Modern Portfolio Theory and Asset Pricing Models Based on Behavioral Insights from Benjamin Graham’s Value Investing Paradigm.

Literary analysis essay

Name

Course

Tutor

Date of Submission

Comparative Literary Analysis of “The Lottery” and “The Tell-Tale Heart” Short Stories

“The Lottery” and “The Tell-Tale Heart” short stories are in one way or another linked through their theme. A theme in a literary work refers to the central idea that the author of that particular work intends to bring out (Marcus and Nichols 629). Notably, the theme comes through different subjects that come from various aspects of human experience including love, death, war, conflicts, and so on.  Therefore, the theme seeks to offer understanding, observation, insight, presentation, and observation of the subjects (Chaitkin 68). Comparatively, themes are akin to the thesis in essays. Looking keenly at the two short stories, it is evident that the theme of death carries the day. In both stories, there is death towards the end of the story. This essay presents a comparative analysis of “The Lottery,” by Shirley Jackson and “The Tell-Tale Heart,” by Edgar Allan Poe through looking at the development of the theme of death through different literary elements such as symbolism, foreshadowing, and point of view.

In both stories, the theme of death is developed through the widespread use of foreshadowing. Foreshadowing is a literary element commonly used by authors to suggest the yet to come plot developments (Stobaugh 420). As a literary element, foreshadowing can be used in developing the theme through placing clues either at the beginning or the middle of a story. Besides, when Old Man Warner talks of corn, it directly indicates that there might be a sacrifice, which in itself must involve death (Jackson). In the case of “The Tell-Tale Heart,” the sentence of the first paragraph by the narrator portends death at the end. The narrator states that “The disease had sharpened my senses–not destroyed–not dulled them (Poe). Above all was the sense of hearing acute. I heard all things in the heaven and in the earth. I heard many things in hell.” It is only at the end where is the mention of the still-beating heart of the old man when it becomes valid as there is the death of Tessie Hutchinson, which is a major theme. In the context of “The Lottery,” the children were packing stones in their pockets and piling them in the square. This is a direct foreshadowing of the death that later materializes. In both cases, Poe and Jackson have successfully used foreshadowing in developing their theme of death.

Another literary element used in the development of the theme of death is symbolism. Symbolism refers to the use of diverse symbols in pieces of literature to exemplify ideas and qualities through giving the symbols unique meanings contrary to their literal meanings (Knowles no pagination; Marcus and Nichols 238). Outstandingly, in both stories, symbolism is widely used to either justify the death or show why death had to occur.  In “The Lottery,” the title itself is symbolic of the seemingly retrogressive traditions that the people are holding and are very reluctant to change. It is held annually and involves death to appease the gods for good harvests after June. There is also another important symbol, the black box, which is also a symbolism of the connection of the people to the tradition. Critically, the black box would also mean evil or death. The names of the characters are also symbolic Mr. Graves signifies the bringer of death, as he helps Mr. Summers in preparing the event through bringing the three-legged stool. Mrs. Delacroix, a French name for the cross, later hurls a huge stone at Tessie Hutchinson despite cordially treating the latter on her later arrival to the venue of the lottery. Still, yet, there is symbolism in the boys gathering round stones which show that the tradition of killing innocent people has to be passed from generation to generation.

On the other hand, in “The Tell-Tale Heart,” the narrator uses the symbol of the eye of the old man is used as a symbol of the essence of the old man and it also has powers. Just like the use of lottery as a rationale to kill the villager who chooses the marked paper, the eye of the old man gives life to the decision of the narrator to kill him (Jackson). According to the narrator, it is the eye that has evil. The eye was revealing something, not about the old man, but about the narrator. The use of the lantern shows the lack of comprehension on the part of the narrator to the extent that the narrator can see the eye. It then fuels the intent of the narrator to murder the old man. In a much similar context, the fact that the black box had been changed and some traditions as well, could have given reason to end the lottery, yet the Old Man Warner is adamant that it cannot be dropped as in other towns. Therefore, it is evident that both foreshadowing and symbolism have been used in developing the theme of death.

In sum, both of the stories have successfully used the literary elements of symbolism and foreshadowing in developing of the theme on death. Most importantly, in the two stories, the death is not natural, and the victims are also innocent. However, despite their innocence, they die because of the held beliefs of their perpetrators. In “The Lottery,” Mrs. Hutchinson died because of tradition while in “The Tell-Tale Heart,” the old man dies on account of the narrator seeing evil in his eyes.

 

 

Works Cited

Chaitkin, Carol. Let’s Review. 4th ed. Hauppauge, NY: Barron’s Educational Series, 2010. Print.

Jackson, Shirley. The Lottery. Mankato: MN Creative Education, 2008. Print.

Knowles, Elizabeth. The Oxford Dictionary of Phrase And Fable. [Oxford]: Oxford University Press, 2005. Print.

Poe, Edgar Allan. “The Tell-Tale Heart.” The Fall of the House of Usher and Other Tales. New York: Signet, 1998. Print.

Marcus, Laura, and Peter Nicholls. The Cambridge History of Twentieth-Century English Literature. Cambridge, UK: Cambridge University Press, 2004. Print.

 

Target Behavior and Outcome Criteria Definition

Case Study Description

A third grade class consists of very rude and undisciplined pupils that the teacher is almost giving up and asking for a transfer. In the past one month, the teacher has been lamenting that if he does not get a transfer to a better school, he would quit teaching and get into business. Upon asking the teacher what the problem was, it was reported that most of the children are disruptive and angry in class. Additionally, the children call each other immoral names, cannot remain on their seats for around five minutes, and cannot follow the set classroom rules even when the teacher calls for their attention. The target behavior would thus be to have the students adhere to the classroom rules, which would lead to an organized classroom.

Target Behavior Definition

While the target behavior is to have an organized classroom, it would involve numerous changes. This means that since there are several numerous target behaviors, the major priority would be by abiding by the classroom rules. It is notable that in all situations, the set classroom rules dictate all the proceedings in the classroom and this ensures respect and peaceful interaction between the teacher and the students. It is therefore through abiding by the set classroom rules that the children would respect each other and call each other by their correct names. This would involve cooperation and respect during class activities since the students would be aware of what is required of them, what is right inside and outside the classroom, and behavior leads to improved cooperation and academic performance (O’Neill & Stephenson, 2014).

In addition, it is through abiding by the set laws that the children would remain in their seats for as long as it is necessary. This would mean that if a teacher needs them to remain seated for the entire class of 30 minutes, they would respect him. This would also call for respecting of the classroom rules since as the teacher gets to a class, there are certain rules that abide his relationship with his students as well as the conduct of the children and the teacher during class hours. Once the children understand their right space in the classroom, stop insulting each other and quit disrespecting the teacher, they would be able to remain seated. This makes abiding by the classroom rules as the first priority and the major reason for all other needed changes (May & Howe, 2013).

The target behavior would thus to have a class of disciplined, attentive, and highly performing children. It is expected that after the applied behavior analysis, the children would be able to seat until the class of 30 minutes is over, adhere to all the classroom rules, stop insulting each other, and be attentive and cooperative in class.  All these required changes are catered for by the classroom rules since they dictate the students’ behaviors and conduct (Kraemer, Davies, Arndt & Hunley, 2012). They are easy to measure rules since the target behavior is to have a child or all the children seated for 30 minutes (for the entire lesson), they would remain seated. If they are out of their seats, it would mean that the target behavior is not achieved. In a similar manner, if the target behavior is for the children to call each other by their correct names, it is expected that no insults or immoral names are used. Attention in class would be measured through listening to the teacher which would be demonstrated through answering to and asking questions as well as reporting high academic performance.

As explained by Boyd, McDonough and Bodfish (2012), the target behaviors should be clearly defined. This would mean that it is easy to distinguish what defines the target behavior and what does not. This means clarification on classroom rules since a class had so many ambiguous rules. In this case, the rules to adhere to are respecting the teacher, calling each other by the right names (not insults), being attentive, and remain seated until a lesson is over. This would make it easy to collect data on the target behavior and be able to make correct and beneficial analysis. It would also make an efficient move of monitoring the progress of the students.

The Social Significance of the Target Behavior

With students who adhere to classroom rules, the first impact would be on the morale of the teacher. As earlier noted, the teacher is almost giving up and is aggressively asking for a transfer. If the classroom does not change, he would be forced to move to another school. His major problem is on the students’ conduct implying that if the students change their behavior, he would be encouraged to teach them. This in turn would persuade the children to look at their lives in a different perspective. They will understand their major aim of being in school and focus it. This would mean improved academic performance and thus bright future of the students. After performing well in school, students are promised of better high schools, colleges, and eventually higher paying and status jobs (Lavigna & Willis, 2012).

It is also notable that performing better in academics is also appropriate for the age of the children. At the age of seven years and in third grade, the children are at an age that cannot be watched when wasting away. It is appropriate that they learn the correct behavior at their age since this would ensure that they grow up as responsible society members. It would also prevent them from landing in jails since with their immoral behaviors, they would later be involved in serious crimes that would land them in jails and other correctional facilities. To avoid problems with the justice system, children need to learn appropriate behaviors at early ages.

Furthermore, performing well in academics would mean that the children live better lives and in better neighborhoods. As earlier noted, when they perform better, they would occupy high paying positions in the top companies. This would mean that they would be able to afford not only their necessities but other luxuries that make life worth living. It is also from what the child earns in future that he would be able to live in a safe neighborhood. In addition, performing well and earning more in top jobs would encourage other children to learn. This would benefit the people in the target behavior because they would live in safe neighborhoods where all children are encouraged to learn rather than join criminality. In the long run, this would mean living in an economically developed country in which very few or no one depends on federal aids.

Outcome Criteria Definition

The target behavior would be measured based on how organized the classroom is. Getting into a classroom in which the expected behavior is evidenced, one wishes to see the children seated until a lesson is over. Upon entering the class, a stranger should see children who call each other by their real names rather than insults. They should also be able to ascertain that they are attentive based on how they answer to the asked questions and how they ask for clarity when the provided information is not adequate. The expected outcome also involves having students who perform better in their academics. Since the students are reported to have been less attentive and disruptive, this can be measured through improved performance. It would be confirmed that the students are attentive enough if they answer the teacher’s questions on covered topics and also remember the information during assignments and tests since this would translate to improved academic performance (Kilian, Hofer & Kuhnle, 2013).

It is also notable that improved academic performance would mean notable harmony in the classroom. For measurement, this would involve getting into the class and getting students well seated, having students respect each other, and lack of physical confrontations in the classroom (Davis, et al., 2014). Since, as a class with students with different personalities, conflicts are inevitable, it would be expected that the students inform the teacher before a physical fight ensues. Further, the behaviors of the students were negatively impacting the morale of the teacher. As a result, progress would involve improved motivation of the teacher. He should look happy with his students and stop his plans of demanding for transfer or quitting his teacher career. After the intervention, it is therefore expected that the teacher would express his gratitude with the changed behavior and how he pleased he is to be a teacher of the third grade students.

 

 

References

Boyd, B. A., McDonough, S. G., & Bodfish, J. W. (2012). Evidence-based behavioral interventions for repetitive behaviors in autism. J Autism Dev Disord., 42(6), 1236-1248.

Davis, T., Durand, S., Fuentes, L., Dacus, S., & Blenden, K. (2014). The effects of a school-based functional analysis on subsequent classroom behavior. Education and Treatment of Children, 37(1), 95-110.

Kilian, B., Hofer, M., & Kuhnle, C. (2013). Conflicts between on-task and off-task behaviors in the classroom: The influences of parental monitoring, peer value orientations, students’ goals, and their value orientations. Social Psychology of Education, 16(1), 77-94.

Kraemer, E., Davies, S., Arndt, K., & Hunley, S. (2012). A comparison of the mystery motivator and the Get ‘Em On Task interventions for off-task behaviors. Psychology in the Schools, 49(2), 163-175.

Lavigna, G., & Willis, T. (2012). The efficacy of positive behavioural support with the most challenging behaviour: The evidence and its implications. Journal of Intellectual and Developmental Disability, 37(3), 185-195.

May, M., & Howe, A. (2013). Evaluating competing reinforcement contingencies on off-task behavior in a preschooler with intellectual disability: A data-based case study. Education and Treatment of Children, 36(1), 97-109

O’Neill, S., & Stephenson, J. (2014). Evidence-based classroom behaviour management content in Australian pre-service primary teacher’ coursework: Wherefore art thou? Australian Journal of Teacher Education, 39(4), 1-22.

Management

Definition of the project goals

Production: The project program seeks to produce 10000 rubber components that suit the supplier’s requirements.

Project scope statement

This project called production of rubber components aims at producing 10,000 rubber components for Poly Products Incorporated. The company has received the Invitation for Suggestion for the built-up of 10,000 rubber products. The goal of the project is to form an accurate plan of operations and manufacturing of the rubber components.

The production project has two activities that have the following scope.

The project seeks to produce 10000 rubber components that must meet the supplier’s requirements. The supplier’s requirements are that the project should be done within 18 months,

Setup:  the quality control program should be acceptable between the two contracting parties, the vendors selected to supply project materials must be licensed for a continuous supply. There will be a flexible material selection conferred to the contractor if he utilizes technology in material testing at all levels. And finally, the project will be based on firm-fixed pricing method that will also see the contractor develop own work breakdown structure upon final approval by the client.

Objectives of the project

  • To create a plan to manufacture 10,0000 rubber elements
  • To study the probable plan that can effect on completion of the manufacturing process of the production project.
  • To increase the ability to manufacture the 10,000 rubber components that relates to the time and cost allocated.

 

Work breakdown structure

According to Snyder, (2013) the practicality of a work breakdown structure is greatly influenced by the production and procurement contractors. Consequently, the cost analysis factor is greatly dependable on the decision these agencies make out of the process. Additionally, a work breakdown structure defines the tasks and milestones that need to be achieved so that the project can meet the deliverables. Thus the structure gives a foundation that project planning, allocation, and tasking of resources are done in a given manner. The following shows how tasks will be broken down into subtasks and later work packages.

Source; Kheder, (2014)

In the above diagram the projects, in this case, will be; project 1; support with tasks such as project office and functional support. The Second project will be pre production that will involve tasks such as research and development and qualification. The third project will be a production with tasks such as setup and production.

Project schedule

 

 

 

 

 

 

 

 

 

 

 

Program Rubber components production
Task Project 1: Support

TASK 1: Project office

TASK 2: Functional support

Project 2: Preproduction

TASK 1: Research & Development

TASK 2: Qualification

Project 3: Production

TASK 1: Setup

TASK 2: Production

Percentage Complete 0%
Prominence Not in progress
Day happening To be confirmed
Day to be finalized To be established
Actual close date To be considered
Task assignment Project Manager,  Project Team
Priority Performance standard for grade 7 employees

Duration is 18 months

Each production should require four months

Rubber components should be manufactured according to client’s specifications.

Milestones  
Notes  

 

 

 

 

 

 

 

 

References

Heldman, K. (2015). PMP project management professional exam deluxe study guide: updated for the 2015 Exam. John Wiley & Sons.

Kerzner, H. (2013). Project management: a systems approach to planning, scheduling, and controlling. John Wiley & Sons.

Kheder, M. (2014). Project Scope Management (Streaming video).  https://www.youtube.com/watch?v=7wvk9DZEgtw  ProjectLibre. (n.d.)

Rose, K. H. (2013). A Guide to the Project Management Body of Knowledge (PMBOK® Guide)—Fifth Edition. Project management journal44(3).

Snyder, C. S. (2013). A project manager’s book of forms: A companion to the PMBOK guide (2nd ed.). Indianapolis, IN Wiley Publishing

 

 

Social Cognitive Theory

The purpose of the study was to determine the relationship of coping style with wellbeing of adolescent prisoners. This was after the reviewed literature revealed that incarcerated adolescents represent a vulnerable group to severe psychological distress. While the adolescents are most likely victims of home violence at young ages while others abuse drugs and alcohol, they suffer from isolation, bullying, and boredom during incarceration. It is notable that some prisoners only experience high levels of distress during their first weeks in prison and later cope with prison life while others maintain significant distress levels resulting to high risks of suicides, depression and anxiety, and self-harm. The study was carried on 133 male adolescent prisoners to determine the effect of coping theories (Brown & Ireland, 2006). According to coping theories, Sharma (2016) argues that distress is moderated by a person’s behavioral and cognitive efforts to reduce the impact of stressors.

The study reported that there were significant decreases in depression and anxiety six weeks after incarceration. It was also reported that as people stay in prisons, emotion coping decreases while detachment coping increases as a result of significant decreases in depression and anxiety. Prisoners who change from emotion to detachment coping have lower distress levels and this is helpful in the context of the initial incarceration period. It was also reported that newly imprisoned adolescents can modify their coping style and this suits specific environmental demands. This theory is applicable to determine how to help prisoners adapt to prison environment or to change prison environment to reduce distress levels. This is because high rates of re-offending are linked to inappropriate coping responses. In addition, prisoners experiencing long-term emotional suppression leads to deleterious effects on psychological and physical health (Brown & Ireland, 2006).

 

 

References

Brown, S. L., & Ireland, C. A. (2006). Coping style and distress in newly incarcerated male adolescents. Journal of Adolescent Health, 38(6), 656-661.

Sharma, M. (2016). Theoretical foundations of health education and health promotion. Burlington, MA: Jones & Bartlett Learning.

 

 

 

Management science

Question 1: Minimax, Laplace Maxmax

There are three possible decisions.

  1. Setting up a plant at Cliff’s end.
  2. Setting up a plant at Manston.
  3. Setting up a plant at Birchington.

Payoffs

Using the output information for each plant, the variable costs and fixed costs were forecasted, as shown in table 2. Since profitability in economics is derived as the difference between total costs and variable costs (Varian & Repcheck, 2010), the fixed costs were amortized over the period of five years, and were then included in the total cost. This total cost was then subtracted from the revenue in table 1 to get the profit, which has been used as the payoff in table 3.

Table 1: Revenue

Revenue (kg) 2018 2019 2020 2021 2022
Cliffs end 100000 108000 116640 125971 136049
Manston 120000 129600 139968 151165 163259
Birchington 140000 147000 154350 162068 170171

 

Table 2: Costs

Fixed cost (Total fixed cost/5)
2018 2019 2020 2021 2022
Cliffs end  £                     30,000.00  £    30,000.00  £    30,000.00  £    30,000.00  £    30,000.00
Manston  £                     34,000.00  £    34,000.00  £    34,000.00  £    34,000.00  £    34,000.00
Birchington  £                     37,000.00  £    37,000.00  £    37,000.00  £    37,000.00  £    37,000.00
Variable cost (kg) (variable costs * number of forecasted units)
2018 2019 2020 2021 2022
Cliffs end  £                           48,000  £          51,840  £          55,987  £          60,466  £          65,303
Manston  £                           54,000  £          58,320  £          62,986  £          68,024  £          73,466
Birchington  £                           60,200  £          63,210  £          66,371  £          69,689  £          73,173

 

Table 3: Payoffs

=Revenue-fixed costs-variable costs 2018 2019 2020 2021 2022
Cliffs end  £                           22,000  £          26,160  £          30,653  £          35,505  £          40,745
Manston  £                           32,000  £          37,280  £          42,982  £          49,141  £          55,792
Birchington  £                           42,800  £          46,790  £          50,980  £          55,378  £          59,997

 

The question assumes that the different states of nature have the same probability of occurrence (0.3). Consequently, the La Place score is £46,960.5 as shown in table 4 below.

The formula is = 0.3* Payoff of each action

Cliffs end  £                       29,040.0  £      33,069.0  £      37,384.4  £      42,007.3  £      46,960.5
Manston  £                       22,440.0  £      25,221.0  £      28,188.6  £      31,355.8  £      34,736.9
Birchington  £                       21,552.0  £      23,957.7  £      26,509.2  £      29,215.7  £      32,087.4

 

Maxmax

=£59,997. This is the highest payoff, as illustrated in table 3.

Maximin

=£42,800. Of all of the payoffs in the different states of nature, this figure is the biggest among the smallest, as shown in table 3.

Question 2: Weighted factor scores

Machines IC Weight 0.2 RC Weight 0.4 EM Weight 0.1 EO Weight 0.2 EI Weight 0.1 Total weighted Score
Score /10 WS Score /10 WS Score /10 WS Score /10 WS Score /10 WS
Gaggia  8 1.6 6 2.4 7 0.7 8 1.6 9 0.9 7.2
Macchina Cioccolato Bosch 7 1.4 9 3.6 8 0.8 8 1.6 8 0.8 8.2
Schokoladen Maschine Callebaut 6 1.2 8 3.2 8 0.8 9 1.8 8 0.8 7.8

Key:

IC = initial cost

RC =Running cost

EM = Ease of maintenance

EO = Ease of operation

EI = Ease of repair

The weights have been assigned up to a limit of 1 (or 100% if converted into percentage). Since Macchina Cioccolato Bosch has the highest weighted score, it is the best machine to use.

Question 3: Linear programme

  1. Chocolate
Ingredient for chocolate Cost per tonne Minimum per tonne Cost per tonne Units per tonne
cocoa butter  $                               3,180 10%  $                         318 0.1
cocoa liquor  $                               3,200 10%  $                         320 0.1
Emulsifier  $                               1,200 1%  $                            12 0.01
Lactose  $                               0.002 50%  $                      0.001 0.5
Sugar  $                                  600 12%  $                            72 0.12
Total  $                         722 0.83

 

Variables

Amount of cocoa butter used = X1

Amount of cocoa liquor used =X2

Amount of emulsifier used= X3

Amount of lactose used = X4

Amount of sugar used = X5

Constraints

Units

0.1X1+0.1X2+0.1X3+0.5X4+0.12X5 ≥0.83 tonnes

Costs

$318 X1+$320 X2+$12 X3+$0.001 X4+ $72X5 ≥ $722

Minimise = 0.1X1+0.1X2+0.1X3+0.5X4+0.12X5

Because these are the minimum acceptable requirements for 1 tonne (1kg) of chocolate, and they are not negotiable since the machine produces batches of 1000kg of chocolate.

Restrictions

X1>0

X2>0

X3>0

X4>0

X5>0

  1. Filings
Filings Minimum portion of the filing Units per 200 litres
Sugar 88% 176
Gelatine 10% 20
Passion fruit essence 2% 4

 

Variables

X1 = Cost of sugar from supplier X

X2 = Cost of gelatine from supplier X

X3= Cost of passion fruit essence from supplier X

Y1 = Cost of sugar from supplier Y

Y2 = Cost of gelatine from supplier Y

Y3= Cost of passion fruit essence from supplier Y

Objective = Minimise X1+X2+X3+Y1+Y2+Y3

Constraints

= 174XY1+20XY2+4XY3 ≥200 units of input

=X1*0.8 + X2*0.2 + X3*0 + Y1*0.9 + Y2*0.05 + Y3*0.05 ≤ £2.45

Since passion essence only contributes up to 5% to the filing, yet increases the unit cost from supplier Y by £46 more than the assumed 2% cost of the passion essence (minimum 2% * the total cost – cost of sugar), reducing the demand for Supplier Y’s product to 5% would reduce the costs drastically, in the model presented below.

=X123*0.95+Y123*0.5.

 

Reference

Varian, H. R., & Repcheck, J. (2010). Intermediate microeconomics: a modern approach (Vol. 6). New York: WW N

 

Site Fixed cost for 5 years Variable cost per Kg Selling price
Cliffs End 150000 0.48 1
Manston 170000 0.45
Birchington 185000 0.43
Forecasts (tonnes)
2018 2019 2020 2021 2022
100 108 117 126 136
120 130 140 151 163
140 147 154 162 170
Weight 0.2 0.4 0.1 0.2 0.1 1 #N/A
Machines Initial cost Weight 0.2 Running cost Weight 0.4 Ease of maintenance Weight 0.1 Ease of operation Weight 0.2 Ease of installation Weight 0.1
Score Total weighted score Total weighted score Total weighted score Total weighted score Total weighted score
Gaggia 8 1.6 6 2.4 7 0.7 8 1.6 9 0.9 7.2
Macchina Cioccolato Bosch 7 1.4 9 3.6 8 0.8 8 1.6 8 0.8 8.2
Schokoladen Maschine Callebaut 6 1.2 8 3.2 8 0.8 9 1.8 8 0.8 7.8
4.2 9.2 2.3 5 2.5
1
cocoa butter  $3,180 10%  $318 318000 0.1 100
cocoa liquor  $3,200 10%  $320 320000 0.1 100
emulsifier  $1,200 2%  $24 24000 0.02 20
lactose  $0.002 55%  $0.001 1 0.55 550
sugar  $600 12%  $72 72000 0.12 120
 $734 0.89
X1
X2 X1 0 X2 0 X3 0 X4 0 X5 0
X3 Minimum amount 100 100 20 550 120
X4
X5 Cost  $318  $320  $24  $0.001  $72
Constraints 0.1 0.02 0.55 0.12
0 <= 1000
 $- <= 722
Minimise