Carla Lee a current MBA student decides to spend her summer

Carla Lee, a current MBA student, decides to spend her summer designing and marketing bicycling maps ofWestern Pennsylvania. She has designed maps, corresponding to three areas 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 three types of maps is:

Print

Cut

Fold

A

1

2

3

B

2

4

2

C

3

1

5

The printer has a limited amount of time in his schedule: 1500 minutes for printing, and 2000 minutes each for cutting and folding.

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. In order to have a sufficiently nice display, at least 100 of each type must be produced.

Use the simplex method to determine the production quantities and projected profit.

Suppose we reduced the 100 limit on one item to 90. Which map should be decreased, and how much more would Carla make?

Solution

The above quantities formalize the problem as below:

A + B + 2C ( we need to maximize this quantity)

constraints for the problem:

with minimum value constraints of each value as 100 i.e.

If the reduction in constraint is reduced from 100 to 90, then the constraint value of B and C will go down to 90 and others will increaseing leading to more manufacturing products for Carla