1 Name:_____________________________ Discussion TA:______________________ Managerial Economics (ARE) 155 University of California, Davis, Fall 2015 Dr. John H. Constantine Quiz 2 (40 points: each question is worth 5 points), Monday, November 2, 2015 There are 3 pages for this quiz. A sandwich shop produces five sandwiches: (i) Tuna, (ii) Tuna and Cheese, (iii) Ham, (iv) Ham and Cheese, and (v) Cheese. The cost the shop incurs to produce each sandwich is found in “Row 6”. The Solver printout to solve this LP problem is given below, The firm’s constraints are found in “Rows 9 to 23”. Also in these rows (9 to 23): Found in “Columns C to G”, are the aij’s. Found in “Column J” are the constrained amount. Found in “Column H” are the amounts of each constraint actually used when producing at the optimal solution. The questions that follow can refer to either the Solver printout given right below or to the Sensitivity analysis found on the following page. B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Unit Cost Constraints/Inputs Bread (slices) Tuna (oz.) Ham (oz.) Cheese (oz.) Mayo (oz.) Mustard (oz.) Lettuce (oz.) Tomato (oz.) Package (unit) Labor (hrs) Minimum Total Sandwiches Min Tuna Sandwiches Min Tuna and Cheese Sandwiches Min Ham Sandwiches Min Ham and Cheese Sandwiches C D E F G Tuna 10 2.42 Tuna/Ch 30 2.12 Ham 10 3.35 Ham/Ch 12 3.02 Cheese 8 2.36 Tuna 2 4 Tuna/Ch 2 3 Ham 2 Ham/Ch 2 Cheese 2 4 1.2 1 0.9 3 1 0.5 0.2 0.25 0.5 1 0.08 1 0.25 0.5 1 0.08 1 1 0.25 0.5 1 0.08 1 0.5 0.2 0.25 0.5 1 0.08 1 1 1 1 4 0.5 0.25 0.5 1 0.08 1 H I J Total Cost 176.42 140 130 76 74 54 4.4 17.5 35 70 5.6 70 10 30 10 12 < < < < < < < < < < > > > > > 140 130 100 80 72 8 20 40 72 8 70 10 12 10 12 2 Sensitivity Report: A B C 6 Variable Cells 7 Cell Name 8 $C$5 Tuna 9 $D$5 Tuna/Ch 10 $E$5 Ham 11 $F$5 Ham/Ch 12 $G$5 Cheese 13 14 15 Constraints 16 Cell Name 17 $H$9 Bread (slices) 18 $H$10 Tuna (oz.) 19 $H$11 Ham (oz.) 20 $H$12 Cheese (oz.) 21 $H$13 Mayo (oz.) 22 $H$14 Mustard (oz.) 23 $H$15 Lettuce (oz.) 24 $H$16 Tomato (oz.) 25 $H$17 Package (unit) 26 $H$18 Labor (hrs) 27 $H$19 Minimum Total Sandwiches 28 $H$20 Min Tuna Sandwiches 29 $H$21 Min Tuna and Cheese Sandwiches 30 $H$22 Min Ham Sandwiches 31 $H$23 Min Ham and Cheese Sandwiches 32 D E F G H Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 10 0 2.42 1E+30 0.38 30 0 2.12 0.24 1E+30 10 0 3.35 1E+30 0.99 12 0 3.02 1E+30 0.66 8 0 2.36 0.66 0.24 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 140 0 140 1E+30 0 130 -0.08 130 24 6 76 0 100 1E+30 24 74 0 80 1E+30 6 54 0 72 1E+30 18 4.4 0 8 1E+30 3.6 17.5 0 20 1E+30 2.5 35 0 40 1E+30 5 70 0 72 1E+30 2 5.6 0 8 1E+30 2.4 70 2.36 70 0 8 10 0.38 10 13.5 10 30 0 12 18 1E+30 10 0.99 10 6 1.5 12 0.66 12 8 2 (a) How much ham does a ham sandwich require? (b) Suppose the firm’s constraint on producing a minimum number of tuna and cheese sandwiches is increased from 12 to 13. How will this impact the firm’s total cost? Briefly explain your result. (c) After the sandwiches are made, how many labor hours remain? Briefly explain your result. There are more questions on the following page. 3 Questions are continued here. (d) Suppose the unit cost for tuna sandwiches increased by $0.50. (i) How does the optimal solution change and (ii) what happens to total cost. Briefly explain your result. (e) Suppose the unit cost for cheese sandwiches decreased by $0.25. (i) How does the optimal solution change and (ii) what happens to total cost? Briefly explain your result. (f) Suppose the quantity of cheese available decreased to 72 ounces. How will this affect (i) the optimal solution and (ii) the total cost? Briefly explain your result. (g) Suppose the shop produced another five sandwiches (from 70 to 75). What will happen to total costs? Briefly explain your result. (h) Suppose the cost of ham sandwiches and cost of ham and cheese sandwiches both decreased by $0.35 simultaneously. How will this affect (i) the optimal solution and (ii) the total cost? Briefly explain your result.