# Operations Management: Optimization and Linear Programming – #226

Question: 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 for bright red, green and pink nail polish bottles combined is at least 50 bottles.

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

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