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 Y_F, Y_S and Y_D 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