(a) Find the revenue function R(q), the profit function P(q), the marginal revenue R'(q), and marginal cost C'(q). Sketch the graphs of P(q), R'(q), and C'(q) on the same coordinate axes and determine the level of production q where P(q) is maximized.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.6: Optimization
Problem 11E: Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the...
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Explanation on question 19.

Complete the whole question, and explain each step. 

(x+ 1)2
MAXIMUM PROFIT AND MINIMUM AVERAGE
COST In Exercises 17 through 22, you are given the
price 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 the revenue function R(q), the profit
function P(q), the marginal revenue R'(q), and
marginal cost C'(q). Sketch the graphs of P(q),
R'(q), and C'(q) on the same coordinate axes
and determine the level of production q where
P(q) is maximized.
(b) Find the average cost A(q)
C(q)
and
sketch the graphs of A(q), and the marginal
cost C'(q) on the same axes. Determine
the level of production q at which A(q) is
minimized.
17. p(q) = 49 - q; C(q) = -q + 4q + 200
%3D
18. p(q) = 37 – 2q; C(q) = 3q² + 5q + 75
%3D
19. p(q) = 180 - 2q; C(q) = q'+ 5q + 162
%3D
Transcribed Image Text:(x+ 1)2 MAXIMUM PROFIT AND MINIMUM AVERAGE COST In Exercises 17 through 22, you are given the price 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 the revenue function R(q), the profit function P(q), the marginal revenue R'(q), and marginal cost C'(q). Sketch the graphs of P(q), R'(q), and C'(q) on the same coordinate axes and determine the level of production q where P(q) is maximized. (b) Find the average cost A(q) C(q) and sketch the graphs of A(q), and the marginal cost C'(q) on the same axes. Determine the level of production q at which A(q) is minimized. 17. p(q) = 49 - q; C(q) = -q + 4q + 200 %3D 18. p(q) = 37 – 2q; C(q) = 3q² + 5q + 75 %3D 19. p(q) = 180 - 2q; C(q) = q'+ 5q + 162 %3D
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