Maximize linear equation with 2 variables

Question

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

Answer 1

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.