Maximizing Profit question

[zanyspydude]

This one is giving me some trouble. Can you help me find the solution?

I will be paid 5$ for every every book I bring to a man. I will be paid an extra $1 per book per box if I bring them in a box.

It will take me 300 minutes to find 1000 books. It will take me 500 minutes to find 1 box.

I have a given number of minutes to return. What is the best strategy to take in order to earn the most?

What I can figure out so far:

let x be the number of books and y be the number of boxes.

Profit = x * ($5 + $1 * y)
Time = 300(x/1000) + 500y

How do I put the two of these together to figure out the max?

 

[zanyspydude]

My attempt at lagrange has gotten me no where:

f(x,y) = x * (5+y)
g(x,y) = 300(x/1000) + 500y

F(x,y) = f(x,y) - lambda(g(x,y) - k)
F(x, y, lambda) = x * (5 + y) - lambda(300/1000x + 500y - k)
F(x, y, lambda) = 5x + xy - 3/10 lambda x - 500 lambda y + lambda k

Fx = 5 + y - 3/10 lambda - 500y = 0
Fy = x - 500 lambda = 0
Flambda = -3/10x - 500y + k = 0