# Linear Programming Problem

• Nov 22nd 2010, 12:16 PM
tbird0041
Linear Programming Problem
Hey guys, I have been trying to teach myself some basic concepts of operations research. I have run across a problem that has been giving me some trouble. Here it is:

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.

I know its a maximization problem and the objective function is Z = .15p + .1c where p is the decision variable for units of PC and c is the decision variable for units of CC.

I start to get a little confused with finding the constraints of the problem. So far I have

9p + 4c <= 36
4p + 4c <= 20

Are there any more constraints? The last sentence confuses me. Does the last sentence mean that I should have additional constraints?
• Nov 22nd 2010, 12:30 PM
pickslides
Quote:

Originally Posted by tbird0041
Are there any more constraints?

what about $p\geq 0 , c\geq 0$
• Nov 22nd 2010, 12:37 PM
tbird0041
yes I would agree with that, I forgot to put those two constraints in the problem because I normally just assume nonegativity, other than those 4 would there be anymore constraints to add?
• Nov 22nd 2010, 12:41 PM
pickslides
I think you have them all, now to maximise z 'profit', test the corner points of the feasible region against the objective function.