A chemical company produces three products: (F)uel, (S)olvent and (D)etergent. Let F , S , and D
Question:
A chemical company produces three products: (F)uel, (S)olvent and (D)etergent. Let F, S, and D represent the amount of each product they produce. They use three limited materials, with constraints:
0.4F + 0.5S + 0.6D ≤ 20 Material 1
0.2S + 0.1D ≤ 5 Material 2
0.6F + 0.3 S + 0.3 D ≤ 21 Material 3
F, S, D ≥0
They also have a setup cost to produce each product and a maximum available production for each product. Specifically:
Product | Profit Margin per unit | Set up cost | Maximum Production |
F | $40 | $200 | 50 |
S | $30 | $50 | 25 |
D | $50 | $400 | 40 |
Let YF, YS and YD be binary variables.
Which objective function and constraints below will we need to add to the above material constraints to best represent this problem as a profit maximization? (2 pts)
A.
Max 40F + 30S + 50D – 200F – 50 S – 400 D
F ≤ 40 YF S ≤ 30 YS D ≤ 50 YD
| B.
Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD
F = 50 YF S = 25 YS D = 40 YD |
C.
Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD
F ≤ 50 YF S ≤ 25 YS D ≤ 40 YD | D.
Max 40F + 30S + 50D – 200YF – 50 YS – 400 YD
F ≤ YF S ≤ YS D ≤ YD |
Statistics for Business and Economics
ISBN: 978-0321826237
12th edition
Authors: James T. McClave, P. George Benson, Terry T Sincich