1. ## Calculating maximum profit

A game company is developing two new games, a board game and a mechanical game. Each board game requires $\frac{1}{2}h$ to manufacture, $\frac{1}{2}h$ to assemble, and $\frac{1}{4}h$ to inspect and package. Each mechanical game requires $1h$ to manufacture, $\frac{1}{2}h$ to assemble, and $\frac{1}{2}h$ 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.

2. Alright, well I think we'd need to set up a series of equations:
First lets just look at the time we have for manufacturing
Let x= amount of board games and y=amount of mechanical games
so:
40=.5x+y
Since we have 40 total hours, each board game takes 1/2 an hour and each mechanical takes one full hour.

Next for the assembly, use the same method:
32=.5x+.5y

Next for the inspection/packaging:
18=.25x+.5y

Lastly for the amount of profit (P):
P=10x+15y

Hopefully that helped...