Course Work Exercise

ABSTRACT

Nowadays, quantitative methods help managers begin the intricate and complex problems of business and industry. These methods can be used to set up resources efficiently, project long-term capital requirements, forecast demand and estimate client preferences. Quantitative methods present an analytical and objective approach to decision making.

In our coursework exercise, theoretically we are the production manager and the company has asked us to specify a manufacturing and purchase plan to meet the demand for the components at a minimum cost.

We are working for the Masters Manufacturing Company and the problem is that our company is planning is planning to satisfy demand of 5,000 units for a stapler in the coming planning period. Each stapler is made of 3 components: a base, a staple cartridge and a handle. Until now Masters has manufactured all 3 components. However the firm may not have enough production capacity to meet all demand and so is considering making an arrangement with another company, Ova Engineering, to make some of the components and Masters will then purchase them. Masters currently have 02 bases, 80 cartridges and no handles in stock, which can be used to help satisfy the demand.

The production time requirements at Masters are given in the following table:

Department Production Time (Hours) Time Available (Hours)

Base Cartridge Handle

Cutting 0.02 0.01 0.04 400

Drilling 0.03 0.01 0.03 400

Finishing 0.01 0.02 0.01 400

The Manufacturing costs at Masters and the purchase costs from Ova are as follows:

Component Manufacturing Cost ($) Purchase Cost ($)

Base 0.65 0.85

Cartridge 0.30 0.45

Handle 1.00 1.30

At the beginning we have to formulate the program as a linear program.

Our variables are:

BM : Number of bases that manufactured

CM : Number of cartridges that manufactured

HM : Number of handles that manufactured

BP : Number of bases that purchased

CP : Number of cartridges that purchased

HP : Number of handles that purchased

MIN 0.65BM+0.30CM+1HM+0.85CP+0.45CP+1.3HP

s.t.

1BM + 1BP = 5000 – 2

1CM + 1CP = 5000-80

1HM + 1HP = 5000

Cutting: 0.02 B + 0.01 C + 0.04 H <= 400

Drilling: 0.03 B + 0.01 C + 0.03 H <= 400

Finishing: 0.01 B + 0.02 C + 0.01H <= 400

BM, BP, CM, CP, HM, HP, >=0

CONSTAINS BASE CARTRIDGE HANDLE LIMITS

PRODUCT B 1 1 4998

PRODUCT C 1 1 4920

PRODUCT H 1 1 5000

CUTTING 0.02 0 0.01 0 0.04 0 400

DRILLING 0.03 0 0.01 0 0.03 0 400