HW3 Table 3.1: Regular & Super Consider the following linear program, which maximizes profit for two products--regular (R) and super (S): Table 3.2: Taco Loco Taco Loco is considering a new addition to their menu. They have test marketed a number of possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products is made from a different combination of beef, beans, and cheese, and each product has a price point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's management science consultant formulates the following linear programming model for company management. MAX 50R + 755 Este 1.2 R +1.6 S 600 assembly (hours) 0.8 R +0.5 S 0 Sensitivity Report: The sensitivity report from the computer model reads as follows: Cell $B$7 $C$7 Name Regular = Super = Super = Final Value 291.67 133.33 Reduced Cost 0.00 0.00 Objective Allowable Allowable Coefficient Increase Decrease 7020 75 50 43.75 Variable Cells Name Cell SE$3 SE$4 SE$5 Final Name Value Assembly (hr/unit) 563.33 Paint (hr/unit) 300.00 Inspect (hr/unit) 100.00 Shadow Price 0.00 33.33 145.83 Constraint RH. Side 600 300 100 Allowable Increase 1E+30 9.29 12.94 Allowable Decrease 36.67 175 40 Cell SC$4 $D$4 SES4 Z Y X Final Value 1. 45 8.36 0 Reduced Cost 0 0 -0.818 Objective Allowable Coefficient Increase 14 0.63 138 17 0.818 Allowable Decrease 5.33 0.56 1E+30 3 Constraints _. and the optimal number of 1) The optimal number of regular products to produce is _ super products to produce is for total profits of_ Answer Cell $F$6 SFS7 SFS8 Name Beef Cheese Beans Final Value 28 80 39.27 Shadow Price 0.45 1 .45 0 Constraint Allowable RH. Side Increase 28 2 80 4 6 6 8 1E+30 Allowable Decrease 1 0.22 5.33 28.73 2) If the company wanted to increase the available hours for one of their constraints (assembly, painting, or inspection) by two hours, they should increase Answer: 6) Taco Loco should try to purchase additional Answer: , but should not buy more 3) The profit on the super product could increase by Answer: without affecting the product mix. 4) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours), profits would be reduced by Answer: 7) Taco Loco should produce both but should not make any Answer: 8) Taco Loco will make the same quantity of X, Y, and Z if the amount of cheese at their disposal is between pounds and pounds. Answer: 5) A change in the market has increased the profit on the super product by $5. Total profit will increase by Answer: 9) For humanitarian reasons, Taco Loco decides they would rather make product X than product Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to accomplish this reversal of demand is