PROBLEM:
The linear programming problem formulation shown below determines how many DVD players, HD TVs, game consoles, and entertainment consoles that an electronics store 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. Constraints 3 and 4 are marketing restrictions.
max 100X1+120X2+150X3+125X4
st
X1 + 2X2 + 2X3 + 2X4 ≤ 108 (constraint 1)
3X1 + 5X2 + X4 ≤ 120 (constraint 2)
X1 + X3 ≤ 25 (constraint 3)
X2 + X3 + X4 ≥ 50 (constraint 4)
For each of the questions below, explain how you arrived at your answer or conclusion.
a. How many of the DVD players, HD TVs, game consoles, and entertainment consoles should be stocked?
b. How much space will be left unused?
c. How much set-up time will be used?
d. By how much will the second marketing restriction be exceeded? What is your conclusion based on?
e. What is the profit that the electronics store will earn?
f. To what value can the profit on DVD players drop before the solution would change?
g. By how much can the amount of display space decrease before there is a change in the profit?
h. Can the electronics store use this solution if the profits on games consoles and entertainment consoles were increased by 10% each?
i. 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?
j. Interpret the dual price of constraint 4.