# Maximize linear equation with 2 variables

How do I maximize the following equation:

$$150 \le 9.05x + 18.89y \\ \text{constraints: } \\ x > 0, y > 0 \\ \text{x and y must be whole numbers.}$$

I cannot use calculus to solve this question, which would have been easy if I could.

go to here: http://imgur.com/qMakA

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What are you trying to maximize? You need some objective function (missing) as well as constraints. –  ncmathsadist Jul 19 '12 at 1:08
its hard enough to explain the problem here because I have it scanned... should I just post a link to the problem? –  Nerd in Training Jul 19 '12 at 1:15
Please attach any material relevant to the question. –  user2468 Jul 19 '12 at 1:22
Honestly, this seems like a silly exercise. I set the price of each bar to be $100. Therefore, I profit. There are no constraints given in the problem statement that govern consumer behavior. – Arkamis Jul 19 '12 at 2:36 add comment ## 1 Answer To solve the problem in your link, what you really want to do is model income and expense. To model expense, define the following variables •$x_c$: the boxes of Zagnut bars bought from cosco •$y_c$: the boxes of Zero bars bought from cosco •$z_c$: the boxes of payday bars bought from cosco •$x_w$: the boxes of Zagnut bars bought from Walmart •$y_w$: the boxes of Zero bars bought from Walmart •$z_w$: the boxes of payday bars bought from Walmart Then, you have that your expenses are$12.49x_c+9.89y_c+18.89z_c+9.05x_w+6.69y_w+4.45z_w \le 150$. Then, you model your income:$p_xn_x+p_yn_y+p_zn_z \ge 350$where$p_x$is the sales price for a Zagnut bar, and$n_x$are the number of bars sold. However, you don't know if you're going to sell out or not; furthermore, there is no information given as to whether your sales rates are affected by$p_w$. If you assume you sell out, then$n_x = 24x_c+18x_w$, and so on. I still don't see this as an optimization problem, however, as there appears to be nothing preventing you from pricing each bar at$1000 and calling it a day.

Community Wiki'd as this is just an extended comment.

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