Date: April 14, 2015

To: James Strong, CEO DC Delco

From: Power-Consulting services

RE: Analysis of the cost of buying versus manufacturing motors for a client.

Foremost we are honored for the opportunity you have given us to offer consultations services to your firm. DC Delco produces three types of motors. The motors require different amount of hours to wire and harness. Therefore, all three types of motors attract different manufacturing costs. In this situation, the company requires a total of 11,700 hours to wire all the motor models. In addition, the company needs a total of 7,900 hours to harness materials for all the three motors. These figures are presented in the table below:

Motor model | Quantity ordered | Wiring time (hours) | Harnessing time (hours) | Total wiring time (hours) | Total harnessing time (hours) |

A | 3000 | 2 | 1 | 6000 | 3000 |

B | 2000 | 1.5 | 2 | 3000 | 4000 |

C | 900 | 3 | 1 | 2700 | 900 |

Total | 5900 | 11,700 | 7900 |

DC Delco has a total of 10,000 hours for wiring and 5000 hours for harnessing. In order to satisfy the needs of the customers and be profitable the company needs to buy some motor units from another vendor. The cost of buying units exceeds the cost of manufacturing thus the need for the company to optimize the cost of buying and manufacturing the units.

We have come up with feasible conclusions based on the information and facts analyzed. These include:

- Cost optimization is necessary in order to maximize the profit will minimize the costs
- DC Delco need to buy some units from the vendor in order to complete the customer’s order

- Recommendations on buying versus manufacturing

Cost optimization

The total of making the motors is:

The cost of buying the motors is:

There is a need to perform cost minimization using linear programming as shown

X is the number of model A motors to be produced

Y is the number of model B motors to be produced

Z is the number of model C motors to be produced

Equation 1 shows the objective function for the problem. The objective is to maximize the number of motors that can be produced by DC Delco before a supplier is contacted to provide the deficit.

The Objective function is subject to a number of conditions. The motor models A, B, and C require 2 hours, 1.5 hours and 3 hours respectively to wire. However, the total available hours are 10,000 hours. Equation 2 shows this information.

Another condition is that the motor models A, B and C require 1 hour, 2 hours, and 1 hour respectively to harness. In addition, the maximum possible harnessing hours available is 5,000 hours. The above information is presented by equation 3.

The last equation, equation 5, shows the non-negativity restriction on the objective function. It means that DC Delco cannot produce negative motors for their customer.

The number of motors to produce and buy

In order to minimize the cost, optimization values from linear programming is shown below

X1 | X2 | X3 | S1 | S2 | P | cost |

5/9 | 0 | 1 | 4/9 | -1/3 | 0 | 2499.999 |

2/9 | 1 | 0 | -2/9 | 2/3 | 0 | 1111.1333 |

122/3 | 0 | 0 | 118/3 | 12 | 0 | 453,333.73 |

The value for x2 that is model B is approximately 2500 motors while that for x3 that is model C motor s is approximately 1112 motors. However, the customer wants 2,000 model 2 and 900 model 3 motors. Therefore, the company will produce 2,000 model B motors and 900 model C motors. On the other hand, DC Delco will buy 3000 model A motors from the supplier.

Producing model B and C will require the following time resources.

Motor Model | Wiring (hours) | Harnessing (hours) |

B | 3000 | 4000 |

C | 2700 | 900 |

Total | 5700 | 4900 |

The cost of producing versus buying

The cost of producing model B motors is:

The cost of producing model C motors is:

The total cost for both motor models is:

The cost of buying motor model A is:

Therefore the total cost of producing and buying is

Recommendations

In order to reduce the cost of production and buying, DC Delco should consider manufacturing both model B and C motors and buying model 1 Motors. The rationale is that the company will utilize the available wiring and harnessing hours efficiently. The available harnessing hours available is 5,000 hours. By manufacturing only model, B and C DC Delco will utilize 4,900 hours of the available 5,000 hours.

It easy cheaper to buy only model A motors since they cost only $ 61 to make compared to model B and C which cost $97 and $145 respectively. The total cost of buying model A and Manufacturing model B and C is $ 466,000. The cost of buying all three models will cost $ 507,500. Thus DC Delco will have a profit of $ 284,000, $41,500 more than when buying all models.

References

Vanderbei, R. (2008). Linear programming foundations and extensions (3rd ed.). New York: Springer.

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