(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 20000 by C(x) = 3x+ .0sxs200. Find the order size that will minimise ordering and storage cost.
(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 20000 by C(x) = 3x+ .0sxs200. Find the order size that will minimise ordering and storage cost.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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
20000
by C(x) = 3x+:
,0Sxs200. 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' – 66q² + 600g + 1000 where q is the output of the firm (in thousands).
(i)
Derive an expression R(q), for the firm' s revenue function.
(ii)
Derive an expression I(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ae692dc-3fb0-4e2c-9b76-e11466feb11a%2F0bfa5a4b-4f77-4df0-96f5-2f3f0bc03115%2Fepx08o_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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
20000
by C(x) = 3x+:
,0Sxs200. 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' – 66q² + 600g + 1000 where q is the output of the firm (in thousands).
(i)
Derive an expression R(q), for the firm' s revenue function.
(ii)
Derive an expression I(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.
Transcribed Image Text: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 Sp is given by
q= 60,p+25+300 for 20s ps100.
(i) Find
da
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)=2 3
I+x*+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
2SI54 determine whether the function f(x) is continuous
throughout its domain?
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