# 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

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.
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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