Marginal Profit Question

crabpot

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Dec 1, 2009
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I'm having trouble setting this problem up, I know that I need to use derivatives but I'm not sure how to setup the initial calculus equation.

A simple item that is to be sold at a small specialty store has $100 in fixed costs and $4 per item in variable costs. The owners assume they can sell 9 items if they charge $55 each, and 5 items at a price of $83 each. For how many units sold/produced is the marginal profit 30 dollars per item?

TIA for the help. :D
 
Marginal Profit is the derivitive of the profit function, it doesn't state that in the problem, though.

It also states that we should use derivitives to find our answer, and that we should assume that the demand function is linear.

Thanks for the help.
 
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