# A company wishes to purchase additional machinery in a capital expansion program. Three types of machinesare to be purchased: A, B, and C. Machine A...

A company wishes to purchase additional machinery in a capital expansion program. Three types of machines

are to be purchased: A, B, and C. Machine A costs USD 25,000 and requires 200 square feet of floor space for its

operation. Machine B costs USD 30,000 and requires 250 square feet of floor space. Machine C costs USD 22,000 and

requires 175 square feet of floor space. The total budget for this expansion program is USD 350,000. The

maximum available floor space for the new machines is 4,000 square feet. The company also wishes to

purchase at least one of each machine.

Given that machines A, B, and C can produce 250, 260, and 225 pieces per day, the company wants to

determine how many machines of each type it should purchase so as to maximize daily output (in units) from

the new machines.

a) Explicitly define your decision variables and formulate the LP model.

b) Assess the validity of the four underlying LP assumptions for this problem.

c) Solve and analyse the problem using a computer package

## Answers

b) Linear / Proportion – the number of units with capital budget and floor space are linearly related.

Deterministic – the coefficients for the variables and constraints are known with certainty.

Additive – Buying one more of a given machine gives more production or additional production. Effect

is additive.

Divisible – This requires that the machines and given constraints to be divisible. In this case the

assumption does not hold. Here we have to take a machine as a whole and not ½ or ¼ or fraction of the

machine.

raphael answered the question on

*January 11, 2019 at 05:37*

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