SOLUTION: you are stenciling wooden boxes to sell at a fair.It takes you 2 hours to stencil a small box and 3 hours to stencil a large box. You make a profit of $10 for a small box and $20

Algebra ->  College  -> Linear Algebra -> SOLUTION: you are stenciling wooden boxes to sell at a fair.It takes you 2 hours to stencil a small box and 3 hours to stencil a large box. You make a profit of $10 for a small box and $20       Log On


   

Question 514025: you are stenciling wooden boxes to sell at a fair.It takes you 2 hours to stencil a small box and 3 hours to stencil a large box. You make a profit of $10 for a small box and $20 for a large box. If you have no more than 30 hours available to stencil and want at least 12 boxes to sell, how many of each size box should you stencil to maximize your profit
Answer by solver91311(24713) About Me  (Show Source):
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Maximize

Subject to:







Note: No need for constraining non-negative since the first two constraints cover that possibility.



Note: Constrain to the integers because you can't make and sell a fractional part of a box in this scenario.

Step 1: Graph the constraint inequalities.

The triangular area where the solution sets overlap is the area of feasibility. The optimum point must be one of the vertices of the feasibility polygon. The integer constraint means that the optimum solution will be an ordered pair of integers that is closest to the ordered pair representing the vertex of the feasibility polygon. In the case of this problem, all three vertices have integer coordinates.

Determine the ordered pairs representing the three vertices of the feasibility triangle and test each one in the Profit function. The one that gives the biggest profit value is the optimum solution.

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John

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