This exercise is based on the following data on three bodybuilding supplements.

Question

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.)

Cell-Tech     serving(s) Riboforce HP     serving(s) cost     $

Explanation / Answer

Please note at first that creatine and taurine have minimun amounts required, while carbohydrates and alpha lipoic acid have maximun amounts that we must not exceed.

As I see it, the limiting step to approach this problem is not to exceed 1200 mg of alpha lipoic acid. Since Riboforce does not contain this compound, we cannot exceed 6 servings of Cell-Tech. In this step we shall consider that creatine reaches 60 g, so we must add 30 g else (or more) from Riboforce HP to reach the minimum required.

If we use 6 servings of each supplement we have:

If we try to reduce 1 serving of Cell-Tech (the most expensive one), we need to add 2 of RiboFOrce HP to compensate creatine levels. Then, we have:

One more reduction gives us:

As we can see, it's impossible to reduce the amount of Cell-Tech without avoing the raise of cost. Therefore, the best formulation we can make is:

6 servings each, at a cost of $22.8 USD.

Servings Creatine (g) Carbs (g) Taurine (g) ALA (mg) Cost (USD) Cell-Tech 6 60 450 12 1200 13.2 RiboForce HP 6 30 90 6 0 9.6 Total 12 90 540 18 1200 22.8

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