You have just been hired as a planner for the municipal school system, and your first assignment is to redesign the subsidized lunch program. In particular, you are to formulate the least expensive lunch menu that will still meet all state and federal nutritional guidelines.  The guidelines are as follows: A meal must be between 500 and 800 calories. It must contain at least 200 calories of protein, at least  200 calories of carbohydrates, and no more than 400 calories of fat. It also needs to have at least 200 calories of a food classified as a  fruit or vegetable.  Table B.3 provides a list of the foods you can consider as possible menu items, with contract-determined prices and nutritional information. Note that all percentages sum to 100% per food—as all calories are protein, carbohydrate, or fat calories. For example, a serving of applesauce has 100 calories, all of which are carbohydrates, and it counts as a fruit/veg food. You are allowed to use fractional servings,  such as 2.25 servings of turkey breast and a 0.33 portion of salad. Costs and nutritional attributes scale likewise: e.g., a 0.33 portion of salad costs $.30 and has 33 calories.  a) Formulate this problem to determine which books should be selected and how many of each should be published to maximize profit.   b) Solve using computer software.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 93P
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You have just been hired as a planner for the municipal school system, and your first assignment is to redesign the subsidized lunch program. In particular, you are to formulate the least expensive lunch menu that will still meet all state and federal nutritional guidelines.  The guidelines are as follows: A meal must be between 500 and 800 calories. It must contain at least 200 calories of protein, at least  200 calories of carbohydrates, and no more than 400 calories of fat. It also needs to have at least 200 calories of a food classified as a  fruit or vegetable.  Table B.3 provides a list of the foods you can consider as possible menu items, with contract-determined prices and nutritional information. Note that all percentages sum to 100% per food—as all calories are protein, carbohydrate, or fat calories. For example, a serving of applesauce has 100 calories, all of which are carbohydrates, and it counts as a fruit/veg food. You are allowed to use fractional servings,  such as 2.25 servings of turkey breast and a 0.33 portion of salad. Costs and nutritional attributes scale likewise: e.g., a 0.33 portion of salad costs $.30 and has 33 calories. 
a) Formulate this problem to determine which books should be selected and how many of each should be published to maximize profit.  
b) Solve using computer software. 

Food Cost/Serving Calories/Serving % Protein % Carbs % Fat Fruit/Veg
Applesauce $0.30  100 0% 100% 0% Y
Canned Corn $0.40  150 20% 80% 0% Y
Fried Chicken $0.90 250 55% 5% 40% N
French Fries $0.20 400 5% 35% 60% N
Mac and Cheese $0.50 430 20% 30% 50% N
Turkey Breast $1.50 300 67% 0% 33% N
Garden Salad $0.90 100 15% 40% 45% Y
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,