Production costs. The graph of the marginal cost function from the production of x thousand bottles of sunscreen per month [where cost C ( x ) is in thousands of dollars per month] is given in the figure. (A) Using the graph shown, describe the shape of the graph of the cost function C ( x ) as x increases from 0 to 8,000 bottles per month. (B) Given the equation of the marginal cost function. C ′ ( x ) = 3 x 2 − 24 x + 53 find the cost function if monthly fixed costs at 0 output are $80,000. What is the cost of manufacturing 4,000 bottles per month? 8,000 bottles per month? (C) Graph the cost function for 0 ≤ x ≤ 8 . [Check the shape of the graph relative to the analysis in part (A).]
Production costs. The graph of the marginal cost function from the production of x thousand bottles of sunscreen per month [where cost C ( x ) is in thousands of dollars per month] is given in the figure. (A) Using the graph shown, describe the shape of the graph of the cost function C ( x ) as x increases from 0 to 8,000 bottles per month. (B) Given the equation of the marginal cost function. C ′ ( x ) = 3 x 2 − 24 x + 53 find the cost function if monthly fixed costs at 0 output are $80,000. What is the cost of manufacturing 4,000 bottles per month? 8,000 bottles per month? (C) Graph the cost function for 0 ≤ x ≤ 8 . [Check the shape of the graph relative to the analysis in part (A).]
Production costs. The graph of the marginal cost function from the production of x thousand bottles of sunscreen per month [where cost C(x) is in thousands of dollars per month] is given in the figure.
(A) Using the graph shown, describe the shape of the graph of the cost function C(x) as x increases from 0 to 8,000 bottles per month.
(B) Given the equation of the marginal cost function.
C
′
(
x
)
=
3
x
2
−
24
x
+
53
find the cost function if monthly fixed costs at 0 output are $80,000. What is the cost of manufacturing 4,000 bottles per month? 8,000 bottles per month?
(C) Graph the cost function for
0
≤
x
≤
8
. [Check the shape of the graph relative to the analysis in part (A).]
The price p (in dollars) and the demand x for a particular clock radio are related by the equation
x=2000−20p.
(A) Express the price p in terms of the demand x, and find the domain of this function.
(B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R?
(C) Find the marginal revenue at a production level of 1200 clock radios.
(D) Interpret R′(1600)=−60.00.
(b) The total revenue curve of a firm is R(g) = 40q- 12q and its
average cost A(q)
q- 12.85q + 20 +
where q is the firm's output.
%3D
30
Derive an expression C(q) for the firm's total cost function.
ii.
Derive an expression II(q) for the firm's profit function.
iii. Is the rate of change of profit increasing or decreasing when the
ouput level of the firm is 10 units?
iv. Determine the level of output for which the firm's profit is maximized.
v. What is the firms's maximum profit?
Fundamentals of Differential Equations and Boundary Value Problems
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