• • • • B.40 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.

Formulate and solve as a linear problem. Print out your formulation in Excel showing the objective function coefficients and constraint matrix in standard form.
◆ Display, on a separate page, the full Answer Report as generated by Excel Solver.
◆ Highlight and label as Z the objective value for the optimal solution on the Answer Report.
◆ Highlight the nonzero decision variables for the optimal solution on the Answer Report.
◆ Display, on a separate page, the full Sensitivity Report as generated by Excel Solver.

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TABLE B.3 Data for Problem B.40 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