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 supply function of a form is given as p=x^2+4x+5. Find the Producer’s Surplus given that the Equilibrium Price is p = 10
The marginal cost of a product can be thought of as the cost of producing one additional unit of output.The marginal cost C in dollars to produce x number of units is given by: C(x) = x2 - 100x + 1500.
(a) How many units should be produced to minimize the marginal cost?
(b) What is the minimum marginal cost?
The price-demand and cost functions for the production of microwaves are given as
p = 235-x/30
c(x) = 52000 + 110x
where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in dollars) of producing x units.
C.) Find the marginal revenue function in terms of x.
E.) Find the profit function in terms of x.
F.) Evaluate the marginal profit function at x=1500.
P'(1500) =
Chapter 5 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Fundamentals of Differential Equations and Boundary Value Problems
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