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# Maximum Profit and Minimum Average Cost

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You are given the function p(q) at which q units of a particular commodity can be sold and the total cost c(q) of producing the q units: In each case

A) Find:
Revenue Function R(q), the profit function P(q), the marginal revenue R'(q), and the marginal cost C'(q). Sketch the graphs of p(q), R'(q), and C'(q) on the same coordinates axes and determine the level of production q where P(q) is maximized.

B) Find:
Average Cost A(q)=C(q)/q and sketch the graphs pf A(q), and the marginal cost C'(q) on the same axes. Determine Level of Production q at which A(q) is minimized.

Given Functions:

1.p(q)=37-2q;C(q)=3q^2+5q+75

2.p(q)=710-1.1q^2;C(q)=2q^3-23q^2+90.7q+151.

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https://brainmass.com/math/optimization/maximum-profit-minimum-average-cost-253895

#### Solution Summary

Step-by-step solution to the maximum profit and minimum average cost is provided in the solution.

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