Anna Broderick is the dietitian for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines for each lunch serving:

●● Between 1,500 and 2,000 calories

●● At least 5 mg of iron

●● At least 20 but no more than 60 g of fat

●● At least 30 g of protein

●● At least 40 g of carbohydrates

●● No more than 30 mg of cholesterol She selects the menu from seven basic food items, as follows, with the nutritional contribution per pound and the cost as given:

Calories

(per lb.)

Iron

(mg/lb.)

Protein

(g/lb.)

Carbohydrates

(g/lb.)

Fat

(g/lb.)

Cholesterol

(mg/lb.) $/lb.

Chicken 520 4.4 17 0 30 180 0.80 Fish 500 3.3 85 0 5 90 3.70 Ground beef 860 0.3 82 0 75 350 2.30 Dried beans 600 3.4 10 30 3 0 0.90 Lettuce 50 0.5 6 0 0 0 0.75 Potatoes 460 2.2 10 70 0 0 0.40 Milk (2%) 240 0.2 16 22 10 20 0.83 The dietitian wants to select a menu to meet the nutritional guidelines while minimizing the total cost per serving.

a. Formulate a linear programming model for this problem.

b. Solve the model by using the computer.

c. If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution? LO.1