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 Decision variables Minimum number of units sold Preparation time per unit (minutes) Profit per unit ($) Tuna mayonnaise Ham and cheese Cheese and salad Spicy vegetable 200 200 200 200 0.40 0.50 0.48 0.55 0.42 0.44 0.35 0.46 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 0 Final Value 790 Original Value Variable Cells Cell Name $B$2 Values T $C$2 Values H $D$2 Values C SE$2 Values S Final Value 400 200 1000 400 0 Constraints Cell Name $F$10 Min. supply (S) $F$11 Proportion (C) $F$12 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>=SH$10 $F$11>=SH$11 $F$12=$H$7 $F$8>=$HS8 $F$9>=$H59 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 0.00671E+30 0.35 0.0913 0.5353 0 .46 0.0913 0.0100 Constraints Final Shadow Value Price 4000 -0.0913 960 0.2667 2000 0.2677 Cell Name SF$10 Min supply (S) $F$11 Proportion (C) $F$12 Prep Time (min.) SF $13 Vending space SF $7 Min. supply (T) SFS8 Min. supply (H) SF 59 Min supply (C) Constraint Allowable Allowable R.H. Side Increase Decrease 200 200 1 E+30 0 375 800 960 30 2000 68.1818 58.2524 200 200 1E+30 200 300 200 200 800 IE.30 30 0 200 -0.0067 10000 Refer to above Excel output ALS is now worried about losing half an hour of preparation time. Joe, the person who currently works only two hours each evening, is aware of this and offered to do an extra hour if Janet reduces her time to 3 hours. How will this impact the optimal solution and the total daily profit, if any? 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 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 decrease by $8.001