Maxima and Minima

Suppose the cost in dollars of making x items of a product is given by C\left(x\right)=10x^{2}+200x+5000.  If the demand function is given by p=f\left(x\right)=2000-5x, how many items should be produced to maximise the profit?  What is the maximum profit?

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 2: Question 15, p. 10)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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