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2. A firm produces two goods, Q1 and Q2. The demand function for Q₁ is: Q₁ = 12- P₁/3, and the demand function for Q2 = 8-P2/5. Meanwhile, the total cost function is TC = Q₁² +2Q1Q2 +3Q₂². a) What are the critical values, or the value of Q1 and Q2 that might maximize the profit, of this firm? b) Use the second order condition to verify that the critical values from a) can maximize the profit of this firm. c) What is the stationary value, or the maximized profit, of this firm?

2. A firm produces two goods, Q1 and Q2. The demand function for Q₁ is: Q₁ = 12- P₁/3, and the demand function for Q2 = 8-P2/5. Meanwhile, the total cost function is TC = Q₁² +2Q1Q2 +3Q₂². a) What are the critical values, or the value of Q1 and Q2 that might maximize the profit, of this firm? b) Use the second order condition to verify that the critical values from a) can maximize the profit of this firm. c) What is the stationary value, or the maximized profit, of this firm?

Advanced Engineering Mathematics
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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2. A firm produces two goods, Q1 and Q2. The demand function for Q₁ is: Q₁ = 12- P₁/3, and the demand function for Q2 = 8-P2/5. Meanwhile, the total cost function is TC =Q₁²+2Q1Q2 + 3Q₂². a) What are the critical values, or the value of Q1 and Q2 that might maximize the profit, of this firm? b) Use the second order condition to verify that the critical values from a) can maximize the profit of this firm. c) What is the stationary value, or the maximized profit, of this firm?
Transcribed Image Text:2. A firm produces two goods, Q1 and Q2. The demand function for Q₁ is: Q₁ = 12- P₁/3, and the demand function for Q2 = 8-P2/5. Meanwhile, the total cost function is TC =Q₁²+2Q1Q2 + 3Q₂². a) What are the critical values, or the value of Q1 and Q2 that might maximize the profit, of this firm? b) Use the second order condition to verify that the critical values from a) can maximize the profit of this firm. c) What is the stationary value, or the maximized profit, of this firm?
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