A game company is developing two new games, a board game and a mechanical game. Each board game requires $\displaystyle \frac{1}{2}h$ to manufacture, $\displaystyle \frac{1}{2}h$ to assemble, and $\displaystyle \frac{1}{4}h$ to inspect and package. Each mechanical game requires $\displaystyle 1h$ to manufacture, $\displaystyle \frac{1}{2}h$ to assemble, and $\displaystyle \frac{1}{2}h$ to inspect and package. In a given week there are 40h available for manufacturing, 32h available for assembly, and 18h for inspection and packaging. Suppose the profit on each board game is $10 and the profit on each mechanical game is $15. How many of each game should be produced each week for maximum profit?

I know how to maximize a function, but I have no idea how to set up the equation for this problem.