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(solution) Susan Chollette, campus dietitian for a small California college,


Susan Chollette, campus dietitian for a small California college, is responsible for formulating a nutritious meal plan for students. For an evening meal, she feels that the following five meal content requirements should be met: (1) between 900 and 1,500 calories; (2) at least 4 milligrams of iron; (3) no more than 50 grams of fat; (4) at least 26 grams of protein; and (5) no more than 50 grams of carbohydrates. On a particular day, Susan's food stock includes seven items that can be prepared and served for supper to meet these requirements. The cost per pound for each food item and its contribution to each of the five nutritional requirements are given in the attachment.
Susan Chollette, campus dietitian for a small California college, is responsible for formulating a

 

nutritious meal plan for students. For an evening meal, she feels that the following five meal

 

content requirements should be met: (1) between 900 and 1,500 calories; (2) at least 4 milligrams

 

of iron; (3) no more than 50 grams of fat; (4) at least 26 grams of protein; and (5) no more than

 

50 grams of carbohydrates. On a particular day, Susan's food stock includes seven items that can

 

be prepared and served for supper to meet these requirements. The cost per pound for each food

 

item and its contribution to each of the five nutritional requirements are given in the table below:

 

Food Item

 

Milk

 

Ground Meat

 

Chicken

 

Fish

 

Beans

 

Spinach

 

Potatoes Calories/Poun

 

d

 

295

 

1216

 

394

 

358

 

128

 

118

 

279 Nutritional Values and Costs

 

Iron

 

Fat

 

Protein Carbohydrate

 

(mg/lb)

 

(g/lb)

 

(g/lb)

 

s (g/lb)

 

0.2

 

16

 

16

 

22

 

0.2

 

96

 

81

 

0

 

4.3

 

9

 

74

 

0

 

3.2

 

0.5

 

83

 

0

 

3.2

 

0.8

 

7

 

28

 

14.1

 

1.4

 

14

 

19

 

2.2

 

0.5

 

8

 

63 Cost/Poun

 

d ($)

 

0.60

 

2.35

 

1.15

 

2.25

 

0.58

 

1.17

 

0.33 a. Set up the Mathematical Model for this Linear Programming (LP) problem.

 

b. Solve the problem using Solver.

 

c. Interpret your solution. You have to interpret the overall objective function; the decision

 

variables; and your constraints.

 


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