A firm makes the same good at two different plants. They have differing costs. The cost of producing in the first plant is C1 = 2q% + 3 The cost of producing in the second plant is C2 = 4q% + 9 The inverse demand functions for this good is as follows: P = 60 – 2Q where Q is total output. The output from the first plant is q1, and the output from the second plant is q2. This means that Q = q1+ q2· Find an expression for the total revenue of the output of each plant. (a) Find an expression for total profit in terms of the output of each plant (q1 and q2). (a) (b) Find the output of each plant which maximise the firm's profit. Check that it is a maximum.
A firm makes the same good at two different plants. They have differing costs. The cost of producing in the first plant is C1 = 2q% + 3 The cost of producing in the second plant is C2 = 4q% + 9 The inverse demand functions for this good is as follows: P = 60 – 2Q where Q is total output. The output from the first plant is q1, and the output from the second plant is q2. This means that Q = q1+ q2· Find an expression for the total revenue of the output of each plant. (a) Find an expression for total profit in terms of the output of each plant (q1 and q2). (a) (b) Find the output of each plant which maximise the firm's profit. Check that it is a maximum.
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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Hi can you please help me to solve Q 9 both c and d I wanna check I have done it correctly, thank you
Transcribed Image Text:9. A firm makes the same good at two different plants. They have
differing costs.
The cost of producing in the first plant is C = 2q% + 3
The cost of producing in the second plant is C2 = 4q2 + 9
The inverse demand functions for this good is as follows:
P = 60 – 2Q where Q is total output.
The output from the first plant is q1, and the output from the
second plant is q2. This means that Q = q1 +q2•
Find an expression for the total revenue of the output of each
plant.
(a)
(a)
Find an expression for total profit in terms of the output of
each plant (q1 and q2).
(b)
Find the output of each plant which maximise the firm's
profit. Check that it is a maximum.
(d)
What are the output levels of each plant if the firm
maximises Total Revenue?
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