Consider the following problem:
A supermarket store manager needs to determine how much to stock of two brands of soda: PC and CC, for Super Bowl Sunday. The store needs to tell the suppliers how many "units" are available and the suppliers then stock the store with their product. Units consist of different flavors and sizes depending on what the suppliers think will sell best. Fractions of units are OK. The store's makes a profit margin of 15 cents for each unit of PC and 10 cents for each unit of CC. In the soda aisle, there is a maximum of 36 linear feet of shelf space: each unit of PC takes up 9 linear feet of shelf space and each unit of CC takes up 4 linear feet of shelf space. In the end displays, there is a 20 linear feet of display space available: each unit of PC takes up 4 linear feet of display space and each unit of CC takes up 4 linear feet of display space. In other words, 1 unit of PC will require 9 feet in the soda aisle plus 4 feet in the end display area.
Problem 1: Set up the problem. What is the objective function? What are the decision variables? What are the constraints?
Problem 2: Solve the problem graphically. Identify all corner point (basic feasible) solutions.
Problem 3: Solve the problem again, this time using the Simplex Method. What is the optimal solution(s)?
In addition to the display area constraints, the manager must meet certain sales quotas from his district manager. The store manager gets 1 point for each unit of PC sold and 4 points for each unit of CC - he must meet a quota of 14 points.
What the district manager doesn't know is that the store manager has a side deal going with the supplier of PC. If the store sells at least half as much PC as CC, the store manager gets tickets to next year's Super Bowl.
Given these two additional constraints, how many units of each brand should the store manager stock?
Problem 4:
Solve the problem with these additional two constraints, using either the LINDO or LINGO software. Using the LINDO or LINGO output (show the output) only and without solving the problem again, answer the following two questions.
- What is the maximum increase in the sales quota without changing the optimal product mix?
- What is the change in the total profit if the profit per unit of PC is increased from 15 to 20