# How to set up a linear programming problem?

I'm not 100% sure if I set up the following problem right. Once I have the problem set up I know how to solve it. (this is a homework problem)

The problem goes like this:"A company can use plastic, aluminum, or a combination of the two to make one of its products. The company cannot use more than 20 units of plastic and must use at least 20 units of aluminum and the cost for the materials cannot exceed $\$$504. If each unit of plastic weighs 5 lbs. and costs \$$6, and each unit of aluminum weighs 30 lbs. and costs$\$$12, how many units of each should they use to have the greatest possible weight?" This is the way I sat up the problem:  Plastic Aluminum Total of units x y of units x < or = 20 y > or = 20 Weigh 5 30 cost  6 12 < or = 504  Maximize: Z=5x+30y Is this the correct way of setting up the problem? Thank you very much. ## 1 Answer If I understand what you've written correctly, you have:$$\begin{align} x&=\text{# of units of plastic} \\ y&=\text{# of units of aluminum} \\ x&\le 20 \\ y&\ge 20 \\ Z&=5x+30y \\ 6x+12y&\le 504 \end{align} and you want to maximize $Z$. This does seem like the correct setup to me. You may want to specify $x\ge 0$, since you cannot have a negative number of units ($y$ is already covered by its minimum of 20).

• Thank you very much, I just needed a second opinion.Thanks again. George – user8805 Mar 28 '11 at 18:29
• @George: You're welcome. If my answer completely answered your question, you can click on the checkmark next to it to mark it as the accepted answer and mark the question as having been answered. – Isaac Mar 28 '11 at 18:58