Carla Lee, a current MBA student, decides to spend her summer designing and marketing bicycling maps of Western Pennsylvania. She has designed 4 maps, corresponding to four quadrants around Pittsburgh. The maps differ in size, colors used, and complexity of the topographical relief (the maps are actually 3-dimensional, showing hills and valleys). She has retained a printer to produce the maps. Each map must be printed, cut, and folded. The requirements (in minutes) and the available time per month (in minutes) to do this for the four types of maps are: | Map A Map B Map C Map D Available Time Print 1 12 3 3 15,000 Cut 2 14 1 3 20,000 Fold 3 2 15 3 20,000 Profit per Map ($) 2 2 2 1 1 The printer has a limited amount of time in his schedule, as noted in the table. In order to have a sufficiently nice display, at least 1000 of each type must be produced. This gives the formulation: A: number of units from map A B: number of units from map B C: number of units from map C D: number of units from map D Max Profit P = 2A + 2B + 1C + 1D Subject to 1 A + 2B + 3 C + 3D= 1000 Minimum Requirements Map A B >= 1000 Minimum Requirements Map B C >= 1000 Minimum Requirements Map C D>= 1000 Minimum Requirements Map D The sensitivity report for this problem is below. Adjustable Cells Final Value Reduced Cost Cell Name $B$13 Decision Variables Map SCS13 Decision Variables Map B SD$13 Decision Variables Map C SES13 Decision Variables Map D 2000 3000 1000 0 0 0 Objective Coefficient 2 2 1 Allowable Increase 1 2 1.75 Allowable Decrease 0.78 0.67 1E+30 1000 0 1 1.25 1E+30 Constraints Shadow Price Final Value 14000 20000 20000 2000 3000 1000 Cell Name SFS5 Printing Time Available LHS SFS6 Cutting Time Available LHS SFS7 Folding Time Available LHS SFSS Minimum Map A LHS SFS9 Minimum Map B LHS SFS10 Minimum Map C LHS $F$11 Minimum Map D LHS 0 0.25 0.5 Constraint R.H. Side 15000 20000 20000 1000 1000 Allowable Increase 1E+30 2000 8000 1000 2000 400 Allowable Decrease 1000 5333.33 2000 1E+30 1 E-30 1000 1000 0 0 -1.75 1000 1000 -1.25 1000 666.67 Answer the following questions: 1. What is the profit? 2. How much is Carla willing to pay for extra cutting time? 3. What is the effect on our solution if the profit per Map A increased from $2 to $4? 4. Suppose that the cutting time decreased from 20,000 to 18,000. What would be the effect on our solution? 5. If the cutting time increased by 100 minutes and the minimum requirements from map C increased by 100 simultaneously, what would be the effect of on our solution