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total cost

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A product can be produced at a total cost C(x) = 800 + 100x^2 + x^3 dollars, where x is the number produced. If the total revenue is given by R(x) = 60,000x - 50x^2 dollars, determine the level of production, x, that will maximize the profit. Find the maximum profit.

A hint was given: P(x) = R(x) - C(x), but I still do not understand how to work the problem.

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Solution Preview

using the hint, profit = revenue - cost,

profit = 60,000x - 50x^2 - 800 - ...

Solution Summary

This solution goes through the concept of total cost as well as maximum profit.