The Westfall Company has a contract to produce 10,000 garden hoses for a large d

Question

The Westfall Company has a contract to produce 10,000 garden hoses for a large discount chain. Westfall has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same.

1

To do:

A. Formulate the optimization problem to minimize total costs.

B. Solve the problem using Lingo.  

C. Explain the solution

Machine Fixed cost to set up Production run Variable cost Capacity

1

750 1.25 6000 2 500 1.5 7500 3 1000 1 4000 4 300 2 5000

Explanation / Answer

Let X(i)= number of hoses produced by machine i, i=1,2,3,4

Y(i)= 1 if machine i is used and 0 if machine i is not used

Objective function:

Minimize Cost

=750Y(1)+500Y(2)+1000Y(3)+300Y(4)+1.25X(1)+1.50X(2)+1.00X(3)+2.00X(4)

Constraints

X(1)<=6000Y(1)

X(2)<=7500Y(2)

X(3)<=4000Y(3)

X(4)<=5000Y(4)

X(1)+X(2)+X(3)+X(4)>=10000

X(1), X(2), X(3), X(4)>=0

X(1), X(2), X(3), X(4) are integres

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