The total revenue curve of a firm is R(q) = 40q − 12q2 and its  average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q ,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

The total revenue curve of a firm is R(q) = 40q − 12q2 and its  average cost A(q) = 1/30q2 − 12.85q + 20 + 400/q ,where q is the firms output.

i. Derive an expression C(q) for the firms total cost function.

ii. Derive an expression Π(q) for the firms profit function.

iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units?

iv. Determine the level of output for which the firms profit is maximized.

v. What is the firmss maximum profit?

Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Area
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,