1. fomulate the LP Model;

2. identify the decision variables used in the model; and

3. determine the optimal solution.

The LP problem determines how many necklaces, bracelets, rings, and earrings a jewelry 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.

LP Problem

Maximize 100x₁+120x₂+150x₃+125x₄

s.t.

x₁+2x₂+2x₃+2x₄ 108

3x₁+5x₂ + x₄ 120

x₁ + x₃ 25

x₂ + x₃+ x₄ 50

x₁, x₂ ,x₃, x₄ 0

Answer the following questions:

a. How many necklaces should be stocked?

b. How many bracelets should be stocked?

c. How many rings should be stocked?

d. How many earrings should be stocked?

e. How much space will be left unused?

f. How much time will be used?

g. By how much will the second marketing restriction be exceeded?

h. What is the profit?

i. To what value can the profit on necklaces drop before the solution would change?

j. By how much can the profit on rings increase before the solution would change?

k. By how much can the amount of space decrease before there is a change in the profit?

l. 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?