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:

- What are the production quantities and projected profit?
- 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?
- Suppose we reduced the 1000 limit on one item to 900. Which map
should be decreased, and how much more would Carla make?
- 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?
- 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?

Mon Aug 24 15:42:04 EDT 1998