Creatine and protein are common supplements in most bodybuilding products. Bodyworks, a nutrition health store, makes...

Creatine and protein are common supplements in most bodybuilding products. Bodyworks, a nutrition health store, makes a powder supplement that combines creatine and protein from two ingredients (X1 and X2). Ingredient X1 provides 20 grams of protein and 5 grams of creatine per pound. Ingredient X2 provides 15 grams of protein and 3 grams of creatine per pound. Ingredients X1 and X2 cost Bodyworks $5 and $7 per pound, respectively. Bodyworks wants its supplement to contain at least 30 grams of protein and 10 grams of creatine per pound and be produced at the least cost. Graphically determine what combination will maximize profits.

Expert Solution

Ans:

To maximize profit,we have to minimize cost.

one pound=454 grams approximately.

(convert per pound cost to per gram cost)

MINIMIZE: Z = 0.011 X1 + 0.015 X2

20 X1 + 15 X2 ≥ 30
5 X1 + 3 X2 ≥ 10

X1, X2 ≥ 0

The problem is unbounded but since it is a minimizing problem can find a solution.

Point	X coordinate (X1)	Y coordinate (X2)	Value of the objetive function (Z)
O	0	0	0
A	0	2	0.03
B	1.5	0	0.0165
C	0	3.33	0.05
D	2	0	0.022

orchestra answered 2 years ago

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