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...