Given Q1 = 150 - 3P1 + P2 + P3 Q2 = 180 + P1 - 4P2 + 2P3 Q3 = 200 + 2P1 + P2 - 5P3 and TC = Q12 + Q1Q2 + 2Q22 + Q2Q3 + Q32 + Q1Q3 a) Find the inverse demand function P = f(Q) and use Cramer’s rule to solve for the critical value Q1 & the critical value Q2. b)Use Cramer’s rule to solve for the critical value Q3.
Given Q1 = 150 - 3P1 + P2 + P3 Q2 = 180 + P1 - 4P2 + 2P3 Q3 = 200 + 2P1 + P2 - 5P3 and TC = Q12 + Q1Q2 + 2Q22 + Q2Q3 + Q32 + Q1Q3 a) Find the inverse demand function P = f(Q) and use Cramer’s rule to solve for the critical value Q1 & the critical value Q2. b)Use Cramer’s rule to solve for the critical value Q3.
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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Given
Q1 = 150 - 3P1 + P2 + P3
Q2 = 180 + P1 - 4P2 + 2P3
Q3 = 200 + 2P1 + P2 - 5P3 and
TC = Q12 + Q1Q2 + 2Q22 + Q2Q3 + Q32 + Q1Q3
a) Find the inverse demand function P = f(Q) and use Cramer’s rule to solve for the critical value Q1 & the critical value Q2.
b)Use Cramer’s rule to solve for the critical value Q3.
c)Calculate the Hessian matrix. What is the value of |H3|? Based on the Hessian, what can you say about the profit?
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