Question

Goodyear Commercial Retread facility recycles worn or damaged tires to retread two sizes of tires, medium and large, for tractor trailers. To fill one client’s order, they will use a combination of three machines to manufacture the retreads and will need to produce at least 54 medium tires and 59 large tires. In one hour, Machine I can produce 2.5 medium tires and 5 large tires, Machine II can produce 4.5 medium tires and 3 large tires, and Machine III can produce 5 medium tires and 10 large tires. The cost per hour to operate Machine I, II, and III are $8, $9, and $10, respectively. There are two combinations of using the three machines that produce the same minimum cost. What are those two combinations and what is the minimum cost?

Answer 1

This problem is solved using Linear Programming.

Let M1, M2, M3 be the number of hours, each machine to be operated.

Objective: Min 8M1+9M2+10M3

s.t.

2.5M1+4.5M2+5M3 >= 54

5M1+3M2+10M3 >= 59

M1, M2, M3 >= 0

Solution using Excel Solver follows:

Formulas:

E2 =SUMPRODUCT(B2:D2,$B$6:$D$6) copy to E2:E4

The optimum combination of operating the three machines is following :

M1 = 0 hours

M2 = 8.167 hours

M3 = 3.45 hours

Minimum cost = $ 108

Another combination is:

M1 = 0 hours

M2 = 2 hours

M3 = 9 hours