A college student on a tight budget wishes to plan a diet which will minimize his food expenditure while maintaining minimum nutritional requirements, according to the Recommended Daily Allowance (RDA). The student wants to plan his menu from the following goods: hamburgers, hot dogs, salad, chicken, pizza, carrots, and cookies. The dietary information (in mg per pound) and cost of each of these foods is as follows:
Nutrient Hamburger Hotdog Salad Chicken Pizza Carrots Cookies RDA
|
Calories
|
2200
|
2100
|
500
|
700
|
2500
|
300
|
2600
|
2500
|
|
Calcium
|
100
|
200
|
400
|
300
|
475
|
400
|
150
|
80 mg
|
|
Protein
|
50
|
70
|
20
|
45
|
35
|
25
|
10
|
25 mg
|
|
Iron
|
25
|
15
|
30
|
10
|
5
|
15
|
20
|
15 mg
|
|
Cost/lb
|
2.50
|
2.00
|
1.75
|
3.00
|
5.00
|
2.25
|
3.50
|
|
Furthermore, assume that the student wants to eat at least 0.25 pounds of cookies each day and will eat at most 0.50 pounds of carrots per day. Formulate an LP model that minimizes daily food expenditures while meeting the RDA and the other constraints given in this problem.