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Derivatives : Demand and Cost Functions

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The marketing research department for a computer company used a large city to test market their new product. They found that the demand equation was p= 1296-0.12 x^2. If the cost equation is C = 830+396 x, find the number of units that will produce maximum profit.

I do not have a price per unit, only the above cost equation.

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Maximum profit is found by applying derivatives to demand and cost equations. The price per units are determined. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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Question :

Find the number of units that will produce a maximum profit.

Problem: The marketing research department for a computer company used a large city to test market their new product. They found that the demand equation was p= 1296-0.12 x^2. If the cost equation is C = 830+396 x, find the number of units that will produce maximum profit.
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