Linear Programming Problems – How to Set Them Up
In my Problem Based Learning Finite Math class this week, we’re doing linear programming problems.
I’ve decided on Tuesdays and Wednesdays to give them a little more guidance (one of the lessons learned from last week). So I’m passing out this handy worksheet on Setting Up Linear Programming Problems.
You can use it too!
Here are the guidance questions that are on the worksheet.
- Write down the “number pieces” of the problem. In other words, get rid of the extra words.
- Write down the units in the problem. These are the things that are being measured – like dollars, grams of items, quantities of items, pounds. Each of these could help you get one of the constraints.
- Write down the question you’re trying to answer. Not all the pieces in the original problem, but just the question. This could help you get the variables.
- Write down what you’re trying to achieve. Usually it’s maximizing or minimizing something. This could help you get the objective function.
- Write down 3 or more situations with real numbers (you make them up) to get a feel for how the problem works.
- Ask yourself some questions about each situation: Did they get enough _____? Did they stay under the amount of _____? What did it cost? Was it too much, not enough or just right?
- For each of the situational questions you asked and answered, ask yourself, “How did I figure it out?” (You can look at the work you did to see or write it out in regular words.) This will help you get the constraints and the objective function.
- Look at everything you’ve done and thought about. This will help you write down the equations. Use the variables you decided in #3. The objective function is the one you want to optimize (from #4) – it usually has an equal sign. The constraints are the ones you graph and shade – they have inequality signs.
Get a copy now!
Don’t bother copying and pasting – you can download the free worksheet here. It’s two pages – perfect to copy double sided and hand out in class!
Let me know how it goes. I’ve used it twice on problems as an alpha test. Hopefully it’ll be helpful to students!
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