How sensitive are turkey breast and applesauce to changes in price. If the constraint for carbs was increased to 300 carbs, would it change the price of the meal? Is the meal balanced?

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Sensitivity report

Answer Report:

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... 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 infor- mation. Note that all percentages sum to 100% per foodas 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 serv- ings, 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. D E F G H A B 1 Microsoft Excel 16.34 Sensitivity Report 2 Worksheet: [LIN P HW.xlsx]Problem 40 3 Report Created: 3/16/20 5:21:10 PM 6 Variable Cells 1 8 10 Cell Name $B$14. A Decision Variable $B$15 CC Decision Variable $B$16 FC Decision Variable $B$17 FF Decision Variable $B$18 M&C Decision Variable $B$19 TB Decision Variable $B$20 GS Decision Variable Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 0 0.172602436 0.3 1E+30 0.172602436 1.333333333 0.4 0.258903654 0.225581395 0.457142857 0.9 0.105071747 0.100581395 0 0.15269103 0.2 1E+30 0.15269103 1.129568106 0.5 0.062909091 0.707833333 0 0.169315615 1. 5 1 E+30 0.169315615 0 0.668150609 0. 9 1 E+30 0.668150609 0 14 15 16 17 Constraints 18 19 Cell Name $D$22 Cost Calories per serving $D$22 Cost Calories per serving $E$22 Cost Protein $F$22 Cost Carbs $G$22 Cost Fat $H$22 Cost Fruit/Veg Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 800 -0.0002299 800 200 251.6129032 8000 500 300 1E+30 200 0.006963455 200 156 40 311.4285714 0 200 111.4285714 1E+30 288.5714286 400 1E+30 111.4285714 200 0.001503876 200 485.7142857 200 24 25 26 27 F G H 6 Engine: Simplex LP 7 Solution Time: 8591965.669 Seconds. 8 Iterations: 6 Subproblems: 0 9 Solver Options 10 Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative 11 12 14 Objective Cell (Min) Cell Name 16 $B$22 Cost Decision Variable Original Value 1.509545958 Final Value 1.509545958 19 Variable Cells Cell Name $B$14 A Decision Variable $B$15 CC Decision Variable $B$16 FC Decision Variable $B$17 FF Decision Variable $B$18 M&C Decision Variable $B$19 TB Decision Variable $B$20 GS Decision Variable Original Value 0 1.333333333 0.457142857 0 1.129568106 Final Value Integer O Contin 1.333333333 Contin 0.457142857 Contin O Contin 1.129568106 Contin O Contin 0 Contin 0 28 31 BO Constraints Cell Name $D$22 Cost Calories per serving $D$22 Cost Calories per serving $E$22 Cost Protein $F$22 Cost Carbs 36 $G$22 Cost Fat 37 $H$22 Cost Fruit/Veg Cell Value Formula Status Slack 800 $D$22=$D$26 Not Binding 300 200 $E$22>=$E$26 Binding 311.4285714 $F$22>=$F$26 Not Binding 111.4285714 288.5714286 $G$22=$H$26 Binding