This exercise is based on the following data on three bodybu

This exercise is based on the following data on three bodybuilding supplements. (Figures shown correspond to a single serving.)

You are thinking of combining Cell-Tech and Riboforce HP to obtain a 10-day supply that provides at least 90 grams of creatine and at least 8 grams of taurine, but no more than 730 grams of carbohydrates and no more than 1,200 milligrams of alpha lipoic acid. How many servings of each supplement should you combine to meet your specifications at the least cost? (If an answer does not exist, enter DNE.)

Solution

*Take into account this: you have to provide enough creatine and taurine, but you can not go above the limits for carbohydrates and acid.

*The cheaper product is definitely Cell-Tech considering what it provides. Then to get a low cost you would think of using specially it.

Let\'s find the 4 inequalities that represent the problem:

*Creatine: 10x+5y>=90
Divide by 5 to obtain 2x+y>=18

*Taurine: 2x+y>=8

Then to satisfy both of them we can choose 2x+y>=18 to represent these requirements.

*Carbohydrates: 75x+15y<=730
Divide by 15 to obtain 5x+y<=146

*Acid: 200x<=1200
Divide by 200 to obtain x<=6

As we said it is cheaper to use Cell-Tech but one of the inequalities says that we can not use more than 6 servings of it. Then we can decide to use the maximum of it x=6.

Now substitute the value in inequalities:

2x+y>=18 and 5x+y<=146

Results in y>=6 and y<=116.

We use the minimum so that it is cheaper. y=6

With x=6 and y=6 we get:

Creatine=90

Taurine=18

Carbohydrates = 540

Acid=600

Then use 6 servings of each, with a cost of 22.8 dollars.