# Linear Programming - Maximizing Profit

1. The linear programming problem whose output follows is used to determine how many bottles of fire red nail polish (x1), bright red nail polish (x2), basil green nail polish(x3), and basic pink nail polish(x4) a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that green nail polish does not require any time to prepare its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for fire red and green polish is 25 bottles, while constraint 4 specifies that the minimum demand combined for bright red, green and pink nail polish bottles is at least 50 bottles.

Please view the attachment for the rest of the solution, which includes all of the required data.

Questions:

a) How many bottles of fire red nail polish, bright red nail polish, basil green polish and pink nail polish should be stocked?

b) What is the maximum profit?

c) How much space will be left unused?

d) How many minutes of idle time remaining for setting up the display?

e) To what value can the per bottle profit on fire red nail polish drop before the solution (product mix) would change?

f) By how much can the per bottle profit on green basil nail polish increase before the solution (product mix) would change?

#### Solution Preview

a) 8 bottles of fire red nail polish, 0 bottles of bright red nail polish, 17 ...

#### Solution Summary

This solution is comprised of a brief, but concise solution which solves each of the required questions using the data provided.