Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.9P
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please answer problem B questions 1 and 2
![8:54 PM
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ECUNIUUS Manemanes jor me sociai sciences I-Course Injormanon. Acaaemic rear zvZIIZULL, Semester i
Problem Set B
(1) If the total cost of a firm is C(x) =1.5x -5x + 20x+5. Find the marginal cost (in dollars)
when 25 units are produced and sold.
(2) The number q of roller blades a firm is willing to sell per week at a price of $p is given by
q = 60,/p+25+300 for 20sp<100.
(i) Find d9
dp
(ii) Find the amount supplied when the price is $56.
(ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.
(3)
(i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S
meters thick at a distance x meters from the break. It difficult to measure the thickness of the
slick directly at the source owing to excess turbulence, but for x>0 they know that
S(x) =
x'+x² +2x
If the oil slick is assumed to be continuously distributed, how thick is expected to be at the
source?
(4x+7
(ii) If f(x) =-
|4x² -1
1sxs2
determine whether the function f(x) is continuous
2<xs4'
throughout its domain?
Problem Set C
(1) Find and classify the extremes value of f(x) =6x* -4x over the interval [-2,2].
(2)
A retailer determines that the cost of ordering and storing units of a product can be modelled by
THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUS
Page 20 of 36
ECONI003 Mathematics for the Social Sciences 1- Course Information. Academic Year 2021/2022, Semester 1
20000
by C(x) - Зх +
,0<x<200. Find the order size that will minimise ordering and storage cost.
(3)
The demand curve of a firm is p=1200- 21q and its total cost is
C(q) = 2q° – 66q + 600q+1000 where q is the output of the firm (in thousands).
(i)
Derive an expression R(g) , for the firm's revenue 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 output level of the firm is
10,000 units?
(iv) Determine the level of output at which profit is maximized.
END OF ASSIGNMINNT](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F178d2fc8-ed91-4adf-95ed-ceaa7e750eeb%2F7d08b54d-4021-4acf-8e59-86bd6c41e783%2Fownatp_processed.png&w=3840&q=75)
Transcribed Image Text:8:54 PM
ECON1003...er 1 (1).pdf - Read-only
ビy
Sign in to edit and save chan...
ECUNIUUS Manemanes jor me sociai sciences I-Course Injormanon. Acaaemic rear zvZIIZULL, Semester i
Problem Set B
(1) If the total cost of a firm is C(x) =1.5x -5x + 20x+5. Find the marginal cost (in dollars)
when 25 units are produced and sold.
(2) The number q of roller blades a firm is willing to sell per week at a price of $p is given by
q = 60,/p+25+300 for 20sp<100.
(i) Find d9
dp
(ii) Find the amount supplied when the price is $56.
(ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.
(3)
(i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S
meters thick at a distance x meters from the break. It difficult to measure the thickness of the
slick directly at the source owing to excess turbulence, but for x>0 they know that
S(x) =
x'+x² +2x
If the oil slick is assumed to be continuously distributed, how thick is expected to be at the
source?
(4x+7
(ii) If f(x) =-
|4x² -1
1sxs2
determine whether the function f(x) is continuous
2<xs4'
throughout its domain?
Problem Set C
(1) Find and classify the extremes value of f(x) =6x* -4x over the interval [-2,2].
(2)
A retailer determines that the cost of ordering and storing units of a product can be modelled by
THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUS
Page 20 of 36
ECONI003 Mathematics for the Social Sciences 1- Course Information. Academic Year 2021/2022, Semester 1
20000
by C(x) - Зх +
,0<x<200. Find the order size that will minimise ordering and storage cost.
(3)
The demand curve of a firm is p=1200- 21q and its total cost is
C(q) = 2q° – 66q + 600q+1000 where q is the output of the firm (in thousands).
(i)
Derive an expression R(g) , for the firm's revenue 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 output level of the firm is
10,000 units?
(iv) Determine the level of output at which profit is maximized.
END OF ASSIGNMINNT
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