Question

Formulate a linear programming problem that can be used to solve the following question:

An individual needs a daily supplement of at least 630 units of vitamin C and 228 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 30 units of vitamin C and 12 units of vitamin E, while each ounce of food II contains 30 units of vitamin C and also 8 units of vitamin E. The total amount of these two foods must be at most 35 ounces. Unfortunately, food I contains 36 units of cholesterol per ounce and food II contains 14 units of cholesterol per ounce. Find the appropriate amounts of the two foods needed so that cholesterol is minimized.

Answer 1

To minimize cholesterol while meeting daily vitamin C and vitamin E requirements, a linear programming problem can be formulated. The appropriate amounts of food I and food II needed to achieve this can be found using this problem. The objective function is to minimize cholesterol intake while subject to constraints on vitamin C, vitamin E, and the total amount of food.

Step-by-step explanation:

This problem can be formulated as a linear programming problem to minimize cholesterol intake while meeting the daily requirements of vitamin C and vitamin E. Let's define the decision variables:

• x1: ounces of food I to consume
• x2: ounces of food II to consume

The objective function to minimize cholesterol intake is:

Minimize Z = 36x1 + 14x2

subject to the following constraints:

• 30x1 + 30x2 ≥ 630 (daily requirement of vitamin C)
• 12x1 + 8x2 ≥ 228 (daily requirement of vitamin E)
• x1 + x2 ≤ 35 (total amount of food)
• x1 ≥ 0, x2 ≥ 0 (non-negativity)

The solution to this linear programming problem will give us the appropriate amounts of food I and food II needed to minimize cholesterol intake while meeting the daily requirements of vitamin C and vitamin E.