joyce and marvin run a day care for preschoolers

joyce and marvin run a day care for preschoolers


 Joyce and Marvin run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They would like to keep their costs down, but also need to meet the nutritional requirements of the children. They have already decided to go with peanut butter and jelly sandwiches, and some combination of graham crackers, milk, and orange juice. The nutritional content of each food choice and its cost are given in the table below:

 

 

Food Item

Calories from fat

Total Calories

Vitamin C (mg)

Protein

(g)

Cost

(¢)

Bread

(1slice)

10

70

0

3

5

Peanut Butter

(1 tbsp)

75

100

0

4

4

Strawberry Jelly

(1 tbsp)

0

50

3

0

7

Graham Cracker

(1 cracker)

20

60

0

1

8

Milk

(1 cup)

70

150

2

8

15

Juice

(1 cup)

0

100

120

1

35

 

The nutritional requirements are as follows. Each child should receive between 400 and 600 calories. No more than the 30% of the total calories should come from fat. Each child should consume at least 60 milligrams (mg) of vitamin C and 12 grams (g) of protein. Furthermore, for practical reasons, each child needs exactly 2 slices of bread (to make the sandwich), at least twice as much peanut butter as jelly, and at least 1 cup of liquid (milk and /or juice).

Joyce and Marvin would like to select the food choices for each child which minimizes cost while meeting the above requirements.

  1. Formulate a linear programming model for this problem.
  2. Solve the problem using Excel. Give the optimal solution and the optimal value.

joyce and marvin run a day care for preschoolers

 Joyce and Marvin run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They would like to keep their costs down, but also need to meet the nutritional requirements of the children. They have already decided to go with peanut butter and jelly sandwiches, and some combination of graham crackers, milk, and orange juice. The nutritional content of each food choice and its cost are given in the table below:

 

 

Food Item

Calories from fat

Total Calories

Vitamin C (mg)

Protein

(g)

Cost

(¢)

Bread

(1slice)

10

70

0

3

5

Peanut Butter

(1 tbsp)

75

100

0

4

4

Strawberry Jelly

(1 tbsp)

0

50

3

0

7

Graham Cracker

(1 cracker)

20

60

0

1

8

Milk

(1 cup)

70

150

2

8

15

Juice

(1 cup)

0

100

120

1

35

 

The nutritional requirements are as follows. Each child should receive between 400 and 600 calories. No more than the 30% of the total calories should come from fat. Each child should consume at least 60 milligrams (mg) of vitamin C and 12 grams (g) of protein. Furthermore, for practical reasons, each child needs exactly 2 slices of bread (to make the sandwich), at least twice as much peanut butter as jelly, and at least 1 cup of liquid (milk and /or juice).

Joyce and Marvin would like to select the food choices for each child which minimizes cost while meeting the above requirements.

  1. Formulate a linear programming model for this problem.
  2. Solve the problem using Excel. Give the optimal solution and the optimal value.