Calculus/calculus

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Question
1. A producer can sell x items per week at a price P=200 - 0.01x kwachas, and it costs C =50x + 20, 000 kwachas to make x items. What is the most profitable number to make?

Answer
Revenue from selling x items :

R(x) = (x)(200-.01x)


Total cost of making x items :

C(x) = 50x + 20,000


Profit from selling x items is revenue minus cost

P(x) = 200x - .01x^2 - 50x - 20,000  

P(x) =  -.01x^2 + 150x - 20,000

The graph is a parabola that opens down , so the maximum occurs where the derivative is 0

P'(x) = -.02x + 150 = 0

.02x = 150

x = 7,500

The answer is 7,500

Calculus

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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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Ph.D. in Mathematics and many years teaching Calculus at state universities.

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B.S. , M.S. , Ph.D.

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