Problem:
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.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to: 1. x1+2x2+2x3+2x4≤108
2. 3x1+5x2+x4≤120
3 .x1+x3≤25
4. x2+x3+x4≥50
x1,x2,x3,x4≥0
optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
1. Sensitivity Analysis 4
How much space will be left unused?
a) 0 b) 5 c) 8 d) 63
2. Sensitivity Analysis 5
By how much can the per bottle profit on green basil nail polish increase before the solution (product mix) would change?
a) 0 b) 5 c) 12 d) 25
3. Sensitivity Analysis 6
What is the lowest value for the amount of time available to setup the display before the solution (product mix) would change?
a) 0 b) 8 c) 57 d) 100
4. Sensitivity Analysis 7
You are offered the chance to obtain more space. The offer is for 15 units and the total price is $1500. What should you do?
a) Accept the offer because the additional profit is greater than the $1500 investment.
b) Reject the offer because the additional profit is less than the $1500 investment.
c) It's a wash, the additional profit is equal to the $1500 investment.