Question

Juan makes two types of wood clocks to sell at local stores. It takes him 2 hours to assemble a pine clock, which requires 1 oz of varnish. It takes 2 hours to assemble an oak clock, which takes 4 oz. of varnish. Juan has 16 oz. of varnish in stock, and can work 20 hours. If he makes $3 profit on each pine clock and $4 on each oak clock, how many of each type should he make to maximize his profits?

Answer 1

Let x the number the number of pine clock and y be the 
number of oak clocks. 
We have the following equations:
$2x+2y\leq20\\x+4y\leq16$
And we wand to do the maximization of the function:
$max(3x+4y)$
The solution, which is a graphical one, is at the point of intersection 
of the two lines, solving the system we get the solution :
x=8, y=2.
Substituting in the function we get the maximal value:
max(f)=24+8=32.