4. A fim is producing three goods and given inverse demand functions are PI=360-6Q1-2Q2- 4Q3, P2-400-2Q1-4Q2, and P3-300-2Q2-6Q3 And Total Cost 2012+2Q2+2Q3? +2Q1Q2+ 2Q2Q3. Now optimize the firm's profit for these three goods using Hessian Method of optimization. First, find all the optimal values of QI, Q2, Q3, and profit using erammer's rule finally show that the profit is optimized (maximized) with these values.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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4. A firm is producing three goods and given inverse demand functions are PI-360-6Q1-2Q2-
4Q3, P2-400-2Q1-4Q2, and P3-300-2Q2-6Q3 And Total Cost 2Q1²+2Q22+2Q3 + 2Q1Q2 +
2Q2Q3. Now optimize the firm's profit for these three goods using Hessian Method of
optimization. First, find all the optimal values of QI, Q2, Q3, and profit using crammer's rule
finally show that the profit is optimized (maximized) with these values.
Transcribed Image Text:4. A firm is producing three goods and given inverse demand functions are PI-360-6Q1-2Q2- 4Q3, P2-400-2Q1-4Q2, and P3-300-2Q2-6Q3 And Total Cost 2Q1²+2Q22+2Q3 + 2Q1Q2 + 2Q2Q3. Now optimize the firm's profit for these three goods using Hessian Method of optimization. First, find all the optimal values of QI, Q2, Q3, and profit using crammer's rule finally show that the profit is optimized (maximized) with these values.
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