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
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:
Next for the inspection/packaging:
Lastly for the amount of profit (P):
Hopefully that helped...