A diet management system produces two types of foods A and B. Food A contains (5,15,1,2) mg. per ounce of cholesterol, calcium, iron and vitamin C respectively and Food B contains (5,15,1,2) mg. per ounce of the same nutrients in order respectively

A nutritionist wishes to minimize the cholesterol content while satisfying the minimum daily requirements (300,13,40) for calcium, iron and vitamin C respectively.

Assume that the number of ounces of the foods used is given by x,y respectively and construct the following:

The function to be minimized is:?

The restriction imposed by vitamin C need is: ? >= ?.

The restriction imposed by calcium need is: ? >= ?.

The restriction imposed by iron need is: ? >= ?.

Is there a typo, both foods have the same nutrition content, so there is no minimization to be done.

Ch(x,y)=5x+5y
C(x,y)=15x+15y≥300
Ca(x,y)=x+y≥13
Fe(x,y)=2x+2y≥40

To construct the function and restrictions, we need to consider the information provided:

Food A contains (5,15,1,2) mg per ounce of cholesterol, calcium, iron, and vitamin C respectively.
Food B contains (5,15,1,2) mg per ounce of the same nutrients in the same order.

The number of ounces of food A used is given by x, and the number of ounces of food B used is given by y.

1. The function to be minimized is the cholesterol content. The cholesterol content of Food A per ounce is 5 mg, and the cholesterol content of Food B per ounce is also 5 mg. Therefore, the function to be minimized is:
Cholesterol Content = 5x + 5y

2. The restriction imposed by vitamin C need is >= 40 mg. The amount of vitamin C in Food A per ounce is 2 mg, and the amount of vitamin C in Food B per ounce is also 2 mg. Therefore, the restriction imposed by vitamin C need is:
2x + 2y >= 40

3. The restriction imposed by calcium need is >= 300 mg. The amount of calcium in Food A per ounce is 15 mg, and the amount of calcium in Food B per ounce is also 15 mg. Therefore, the restriction imposed by calcium need is:
15x + 15y >= 300

4. The restriction imposed by iron need is >= 13 mg. The amount of iron in Food A per ounce is 1 mg, and the amount of iron in Food B per ounce is also 1 mg. Therefore, the restriction imposed by iron need is:
1x + 1y >= 13

In summary:

The function to be minimized is: Cholesterol Content = 5x + 5y

The restriction imposed by vitamin C need is: 2x + 2y >= 40

The restriction imposed by calcium need is: 15x + 15y >= 300

The restriction imposed by iron need is: 1x + 1y >= 13