LP: Certain Sensitivity Analysis Questions must be answered based on the Excel Output below. The sandwich company, Alamo Lone Star (ALS) prepares sandwiches for sale in vending machines in various locations of an urban area. The four types of sandwich that are now provided are those that have been found to sell well. The following information is available on each type: Type of sandwich Minimum number of units sold Preparation time per unit Decision variables Profit per unit ($) 200 200 I Tuna mayonnaise Ham and cheese Cheese and salad Spicy vegetable 0.40 0.50 0.48 0.55 0.42 0.44 0.35 0.46 200 200 The most popular sandwich is the cheese and salad so ALS ensure that at least half of all sandwiches supplied are cheese and salad. All four types of sandwich are prepared each evening and then distributed to the vending machines the next morning. Sandwich preparation is carried out by five part-time workers. Four of these workers each work 3.5 hours each evening and one works for only two hours. ALS has 50 identical sandwich vending machines each with a capacity of 40 units. The manager of ALS needs to know how many of each type of sandwich they should produce each evening to maximize profit, subject to unit profit figures and constraints mentioned above. This problem was formulated as a linear programming model and then solved using Excel Solver. The Excel Solver output is provided below. Please note that to keep the model as simple as possible, it was assumed that ALS can sell all sandwiches they produced APPENDIX Below is the Excel Solver output. Note that the cell entry 1E+30 means an unlimited amount. Objective Cell (Max) Cell Name $F$4 Max Profit Original Value Final Value 790 Original Value Variable Cells Cell Name SB$2 Values T $C$2 Values H $D$ 2 Values C $E$2 Values S 0 Final Value 400 200 1000 400 0 Constraints Cell Name SF$10 Min. supply (S) SF$11 Proportion (C) SFS12 Prep. Time (min.) SFS13 Vending space $F$7 Min. supply (T) $F$8 Min. supply (H) $F$9 Min. supply (C) Cell Value 400 0 960 2000 400 200 1000 Formula $F$10>=SHS10 $F$11>SH$11 $F$12=$H$7 $F$8>=SH$8 $F$9>=SH$9 Status Not Binding Binding Binding Binding Not Binding Binding Not Binding Slack 200 0 0 0 200 0 800 Variable Cells Cell $B$2 $C$2 $D$2 SE$2 Name Values T Values H Values C Values S Final Reduced Value Cost 400 0 200 0 10000 400 0 Objective Allowable Allowable Coefficient increase Decrease 0 .42 0.0400 0.0200 0 .44 0.0067 1E+30 0 .35 0.0913 0.5353 0 .46 0.0913 0.0100 Constraints Cell Name $F$10 Min supply (S) $F$11 Proportion (C) $F$12 Prep. Time (min.) $F$13 Vending space $F$7 Min. supply (T) $F$8 Min. supply (H) $F$9 Min supply (C) Final Value 400 D 960 2000 400 200 1000 Shadow Price 0 -0.0913 0.2667 0.2677 Constraint Allowable Allowable R.H. Side Increase Decrease 200 200 1E+30 0 375 800 960 30 30 2000 68.1818 58.2524 200 200 1 E+30 200 300 200 200 800 1 E+30 -0.0067 0 Refer to above Excel output, Janet, one of the four workers who work 3.5 hours each evening, wishes to reduce her time to 3 hours. What effect will this change have on the optimal solution and the total daily profit. if any? This change is not allowed. Thus, the optimal solution will remain the same. The model has to be rerun to find out the new optimal daily profit. This change is not allowed. Thus, the optimal solution and the total daily profit will change. The model has to be rerun. This change is allowed. The optimal solution will remain the same but the optimal daily profit will increase by $8.001. This change is allowed. The optimal solution and the total daily profit will not change. This change is allowed. The optimal solution will remain the same but the optimal daily profit will decrease by $8.001