AP37. The production function f(x) gives the number of units of an item that a manufacturing company can produce from x units of raw material. The company buys the raw material at price w dollars per unit and sells all it produces at a price of p dollars per unit. The quantity of raw material that maximizes profit is denoted by x. (a) Do you expect the derivative f'(x) to be positive or negative? Justify your answer. (b) Explain why the formula r(2) = pf(a)- wa gives the profit r(z) that the company earns as a function of the quantity x of raw materials that it uses. (c) Evaluate f'(x"). (d) Assuming it is nozero, is f"(x') positive or negative? (e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat x as a function of w. Find a formula for the derivative dx'/dw and decide whether it is positive or negative. (f) If the price w goes up, should the manufacturing company buy more or less of the raw material?
AP37. The production function f(x) gives the number of units of an item that a manufacturing company can produce from x units of raw material. The company buys the raw material at price w dollars per unit and sells all it produces at a price of p dollars per unit. The quantity of raw material that maximizes profit is denoted by x. (a) Do you expect the derivative f'(x) to be positive or negative? Justify your answer. (b) Explain why the formula r(2) = pf(a)- wa gives the profit r(z) that the company earns as a function of the quantity x of raw materials that it uses. (c) Evaluate f'(x"). (d) Assuming it is nozero, is f"(x') positive or negative? (e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat x as a function of w. Find a formula for the derivative dx'/dw and decide whether it is positive or negative. (f) If the price w goes up, should the manufacturing company buy more or less of the raw material?
Chapter3: Functions
Section3.2: Domain And Range
Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...
Related questions
Question
Transcribed Image Text:AP37. The production function f(x) gives the number of units of an item that a manufacturing company can
produce from x units of raw material. The company buys the raw material at price w dollars per unit and
sells all it produces at a price of p dollars per unit. The quatity of raw material that maximizes profit is
denoted by x'.
(a) Do you expect the derivative f'(x) to be positive or negative? Justify your answer.
(b) Explain why the formula 7(x) = pf(x)- wz gives the profit (z) that the company earns as a
function of the quantity x of raw materials that it uses.
(c) Evaluate f'(x").
(d) Assuming it is nozero, is f"(x) positive or negative?
(e) If the supplier of the raw materials is likely to change the price w, then it is appropriate to treat x
as a function of w. Find a formula for the derivative dx"/dw and decide whether it is positive or
negative.
(f) If the price w goes up, should the manufacturing company buy more or less of the raw material?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning