SOLUTION: You are stenciling wooden boxes to sell at a craft fair. It takes you 3 hours to stencil a small box and 6 hours to stencil a large box. You make a profit of $12 for a small box

Question 1172192: You are stenciling wooden boxes to sell at a craft fair. It takes you 3 hours to stencil a small box and 6 hours to stencil a large box. You make a profit of $12 for a small box and $16 for a large box. If you have no more than 30 hours available to stencil and don’t plan to have more than 11 boxes completed, how many of each size box should you stencil to maximize profits?

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Not a good example of this kind of problem, since the given information makes a solution by logical reasoning easy....

The 3 hours to stencil a small box and the 6 hours to stencil a large box, along with the total 30 hours available, makes the maximum possible number of boxes 30/3 = 10, so the condition that the number of boxes must be no more than 11 is superfluous.

Then, since the time for stenciling a large box is twice the time for stenciling a small box, whereas the profit from a large box is LESS THAN twice the profit from a small box, makes it obvious that the maximum profit is by stenciling only small boxes.

ANSWER: The maximum profit is by stenciling 30/3 = 10 small boxes (and 0 large boxes).

Answer by ikleyn(52814) (Show Source): You can put this solution on YOUR website!
.

Making a large box in 6 hours at $16 profit CAN NOT compete with making a small box in 3 hours at $12 profit.

So, the right strategy is to make small boxes only and do not make large boxes, at all.

By doing this way, you will make 30/3 = 10 small boxes profiting 10*12 = 120 dollars.

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