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You are stenciling wooden boxes to sell at a fair. Stenciling takes 2 hours for a small box and 3 hours for a large box. Profit for a small box is $10 and $20 for a large box. If
you have no more than 30 hours available to stencil, but want at least 12 boxes to sell, how many of each size box should you sell to maximize your profit? (x = small boxes
and y large boxes)
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raphealnwobi raphealnwobi · Answer 1 · 2021-11-03T10:25:45+01:00

The number of stenciled wooden boxes needed so as to maximize profit is 6 small boxes and 6 large boxes.

Let x represent small boxes and y represent large boxes.

Since you have no more than 30 hours available to stencil, hence:

2x + 3y ≤ 30

Also, at least 12 boxes are required to sell, hence:

x + y ≥ 12

The solution to this problem gives:

x = 6, y = 6

Hence 6 small boxes and 6 large boxes are needed.

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