Carla's Maps

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 time (in minutes) to do this for the four types of maps is:

The printer has a limited amount of time in his schedule, as noted in the table.

The profit per map, based on the projected selling price minus printers cost and other variable cost, comes out to approximately $1 for A and B and $2 for C and D. In order to have a sufficiently nice display, at least 1000 of each type must be produced.

This gives the formulation:

 
 MAX     A + B + 2 C + 2 D
 SUBJECT TO
           A + 2 B + 3 C + 3 D <=   15000
           2 A + 4 B + C + 3 D <=   20000
           3 A + 2 B + 5 C + 3 D <=   20000
           A >=   1000
           B >=   1000
           C >=   1000
           D >=   1000

Attached is the Solver output.

Adjustable Cells							
               Final        Reduced Objective     Allowable  Allowable
Cell   Name    Value        Cost    Coefficient   Increase   Decrease
$B$11   XA       1500           0          1            1      0.333333
$B$12   XB       1000           0          1     0.333333         1E+30
$B$13   XC       1000           0          2     0.333333         1E+30
$B$14   XD   2833.333           0          2            1           0.5

Constraints                     
                    Final        Shadow       Constraint Allowable  Allowable
   Cell   Name      Value        Price        R.H. Side  Increase   Decrease
   $B$17   Print     15000         0.5         15000         100   366.6667
   $B$18   Cut       16500           0         20000       1E+30       3500
   $B$19   Fold      20000    0.166667         20000        7000       1000
   $B$20   MinA       1500           0          1000         500      1E+30
   $B$21   MinB       1000   -0.333333          1000        1750       1000
   $B$22   MinC       1000   -0.333333          1000         500       1000
   $B$23   MinD   2833.333           0          1000    1833.333      1E+30

Here are some questions to answer:

1. What are the production quantities and projected profit?

2. How much is Carla willing to pay for extra printing time? cutting time? folding time? For each, how many extra hours are we willing to buy at that price?

3. Suppose we reduced the 1000 limit on one item to 900. Which map should be decreased, and how much more would Carla make?

4. A fifth map is being thought about. It would take 2 minutes to print, 2 minutes to cut, and 3 minutes to fold. What is the least amount of profit necessary in order to consider producing this map? What is the effect of requiring 1000 of these also?

5. The marketing analysis on D is still incomplete, though it is known that the profit of $2 per item is within $.25 of the correct value. It will cost $500 to complete the analysis. Should Carla continue with the analysis?