Question

An individual needs a daily supplement of at least 464 units of vitamin C and 252 of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 32 units of vitamin C and 9 units of vitamin E, while each ounce of food II contains 16 units of vitamin C and also 18 units of vitamin E. The total supplement of these two foods must be at most 35 ounces. Unfortunately, food I contains 48 units of cholesterol per ounce and food II contains 25 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. Find the minimum amount of cholesterol.

Answer 1

z (min) = 705

x₁ = 10

x₂ = 9

Explanation:

Let´s call x₁ quantity of food I ( in ou ) and x₂ quantity of food II ( in ou)

units of vit. C units of vit.E Cholesterol by ou

x₁ 32 9 48

x₂ 16 18 25

Objective function z

z = 48*x₁ + 25*x₂ To minimize

Subject to:

1.-Total units of vit. C at least 464

32*x₁ + 16*x₂ ≥ 464

2.- Total units of vit. E at least 252

9*x₁ + 18*x₂ ≥ 252

3.- Quantity of ou per day

x₁ + x₂ ≤ 35

General constraints x₁ ≥ 0 x₂ ≥ 0

Using the on-line simplex method solver (AtoZmaths) and after three iterations the solution is:

z (min) = 705

x₁ = 10

x₂ = 9