A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling, finishing, and packaging model A are 3 hours, 3 hours, and 0.8 hour, respectively. The times for model B are 4 hours, 2.5 hours, and 0.4 hour. The total times available for assembling, finishing, and packaging are 6000 hours, 4200 hours, and 950 hours, respectively. The profits per unit are $500 for model A and $575 for model B. What is the optimal production level for each model?

Question

model A

model B

What is the optimal profit?
$

Answer 1

For x of A and y of B, you want to

maximize p=550x+575y subject to
3x+4y <= 6000
3x+2.5y <= 4200
0.8x+0.4y <= 950

now just use your favorite linear algebra solver to get the answer.

Answer 2

6400