Question 3 Assume that the quantities of two products (A and B) produced by a multi-product firm are given by the functions Qa = 10PB – 10PA. QB = 100 + 10PA – 20Pn. where Qa, QB, PA and Pg denote respectively, the quantity of A produced, the quantity of B produced, the price per unit (in dollars) of A, and the price per unit (in dollars) of B. The average cost of producing one unit of A is $1, and the average cost of producing one unit of B is $2. (1) Derive the total profit of the firm as a function of Pa and Pg. (2) Find Pa and Pg that maximise the firm's total profit. (3) Calculate quantity values of Qa and Qp at the prices that maximises the firm's total profit.
Question 3 Assume that the quantities of two products (A and B) produced by a multi-product firm are given by the functions Qa = 10PB – 10PA. QB = 100 + 10PA – 20Pn. where Qa, QB, PA and Pg denote respectively, the quantity of A produced, the quantity of B produced, the price per unit (in dollars) of A, and the price per unit (in dollars) of B. The average cost of producing one unit of A is $1, and the average cost of producing one unit of B is $2. (1) Derive the total profit of the firm as a function of Pa and Pg. (2) Find Pa and Pg that maximise the firm's total profit. (3) Calculate quantity values of Qa and Qp at the prices that maximises the firm's total profit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Question 3
Assume that the quantities of two products (A and B) produced by a multi-product firm
are given by the functions
Qa = 10Pn – 10PA.
QB = 100 + 10PA – 20PB.
where Qa, QB, PA and Pg denote respectively, the quantity of A produced, the quantity
of B produced, the price per unit (in dollars) of A, and the price per unit (in dollars) of B.
The average cost of producing one unit of A is $1, and the average cost of producing
one unit of B is $2.
(1) Derive the total profit of the firm as a function of Pa and Pg.
(2) Find Pa and Pg that maximise the firm's total profit.
(3) Calculate quantity values of Qa and Qn at the prices that maximises the firm's total
profit.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
