1) Ask yourself the question: What might I do? Over what parameters of this problem do I have control?
2) Realize that each of these things you might do is a variable, and give that variable a name:
3) Determine, for each of the things you MIGHT do, what type of answer should result for each of the variables.
Floating point? Integer? Binary?
4) Write a bill or a profit statement. Basically, what is desired by this problem? What is your TRUE objective?
You will find it far simpler to generate your MIN/MAX statement using the following procedure:
1) Blindly write down a list of all of your variables. Include them all:
VARIABLEab + VARIABLEac + VARIABLEad + … + VARIABLEzz|
2) Add MIN Z = or MAX Z in front, depending on what you are trying to do, and multiply each variable times its unit cost or profit:
MIN Z = COSTab*VARIABLEab + COSTac*VARIABLEac + COSTad*VARIABLEad + … + COSTzz*VARIABLEzz
or MAX Z = PROFITab*VARIABLEab + PROFITac*VARIABLEac + PROFITad*VARIABLEad + … + PROFITzz*VARIABLEzz
In other words simply list all of your variables in a MAX/MIN statement, one at a time, then go back in and precede them by their unit costs or profits. This will give you the final total bill or profit that will result no matter what the final answer for each variable turns out to be.
5) List any constraints or requirements specified by the contract or governing agency. These constraints are known as “Subject To’s” in linear programming. What conditions MUST be satisfied for the solution you derive to be acceptable. What conditions SHOULD be satisfied for the solution you derive to be acceptable? What conditions WOULD BE NICE to be satisfied for the solution you derive to be acceptable?
6) Draw a sketch of the problem. Label all the variables, costs, constraints on this sketch.
7) Note that these problems cannot be solved using Engineering Equation Solver. They are best solved using MOR or some other LP program. They can be solved using Excel, but MOR is better. Also, hand solutions to LP problems are not really feasible. You just have to check the computer solution as best you can and be careful.