HW Supplement: Marginal Analysis Name 1. The total weekly cost (in dollars) in producing x 3-D printed doghouses is given by C(x) = 20,000+20x-.001x2 (0 ≤ x ≤6000). a. Sketch a graph the Total Cost function. Window? Try x[0,6000] y[0, 100,000]. b. Find the Marginal Cost function. C'(x) c. What is the marginal cost when x=1000? d. The marginal cost is an estimate for the cost of producing an additional item given a "present production number." So, (c) gives an estimate for the cost of producing 1 more doghouse if production is currently at 1000. Find the actual cost to produce the 1001st doghouse and compare to your answer in (c). e. Find the Average Cost function, C(x). (Simplify by distributing your division) f. Find the Marginal Average Cost function, C '(x). g. Argue that C '(x) is never zero so must have the same sign on the whole interval (0, 6000]. What is that sign? Interpret your results. Bonus: What is it about the total cost curve that makes the estimate in (c) so darn close to the actual cost in (d)?
HW Supplement: Marginal Analysis Name 1. The total weekly cost (in dollars) in producing x 3-D printed doghouses is given by C(x) = 20,000+20x-.001x2 (0 ≤ x ≤6000). a. Sketch a graph the Total Cost function. Window? Try x[0,6000] y[0, 100,000]. b. Find the Marginal Cost function. C'(x) c. What is the marginal cost when x=1000? d. The marginal cost is an estimate for the cost of producing an additional item given a "present production number." So, (c) gives an estimate for the cost of producing 1 more doghouse if production is currently at 1000. Find the actual cost to produce the 1001st doghouse and compare to your answer in (c). e. Find the Average Cost function, C(x). (Simplify by distributing your division) f. Find the Marginal Average Cost function, C '(x). g. Argue that C '(x) is never zero so must have the same sign on the whole interval (0, 6000]. What is that sign? Interpret your results. Bonus: What is it about the total cost curve that makes the estimate in (c) so darn close to the actual cost in (d)?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![HW Supplement: Marginal Analysis
Name
1. The total weekly cost (in dollars) in producing x 3-D printed doghouses is given by
C(x) = 20,000+20x-.001x2 (0 ≤ x ≤6000).
a. Sketch a graph the Total Cost function. Window? Try x[0,6000] y[0, 100,000].
b. Find the Marginal Cost function. C'(x)
c. What is the marginal cost when x=1000?
d. The marginal cost is an estimate for the cost of producing an additional item given a "present
production number." So, (c) gives an estimate for the cost of producing 1 more doghouse if
production is currently at 1000. Find the actual cost to produce the 1001st doghouse and
compare to your answer in (c).
e. Find the Average Cost function, C(x). (Simplify by distributing your division)
f. Find the Marginal Average Cost function, C '(x).
g. Argue that C '(x) is never zero so must have the same sign on the whole interval (0, 6000].
What is that sign? Interpret your results.
Bonus: What is it about the total cost curve that makes the estimate in (c) so darn close to the actual
cost in (d)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0aafe4d-d53d-4245-bfd6-73a95d183b3c%2F9589f34a-1007-4bae-95c9-182e5c099a90%2F7dbx6vs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:HW Supplement: Marginal Analysis
Name
1. The total weekly cost (in dollars) in producing x 3-D printed doghouses is given by
C(x) = 20,000+20x-.001x2 (0 ≤ x ≤6000).
a. Sketch a graph the Total Cost function. Window? Try x[0,6000] y[0, 100,000].
b. Find the Marginal Cost function. C'(x)
c. What is the marginal cost when x=1000?
d. The marginal cost is an estimate for the cost of producing an additional item given a "present
production number." So, (c) gives an estimate for the cost of producing 1 more doghouse if
production is currently at 1000. Find the actual cost to produce the 1001st doghouse and
compare to your answer in (c).
e. Find the Average Cost function, C(x). (Simplify by distributing your division)
f. Find the Marginal Average Cost function, C '(x).
g. Argue that C '(x) is never zero so must have the same sign on the whole interval (0, 6000].
What is that sign? Interpret your results.
Bonus: What is it about the total cost curve that makes the estimate in (c) so darn close to the actual
cost in (d)?
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