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A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q, + 10Q2 where Q, and Q, denote the quantities of G1 and G2 respectively. If P, and P, denote the corres- ponding prices then the demand equations are P = 50 – Q1 - Q2 P2 = 100 – Q, - 4Q2 Find the maximum profit if the firm's total costs are fixed at $100. Estimate the new optimal profit if total costs rise by 7%.

A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q, + 10Q2 where Q, and Q, denote the quantities of G1 and G2 respectively. If P, and P, denote the corres- ponding prices then the demand equations are P = 50 – Q1 - Q2 P2 = 100 – Q, - 4Q2 Find the maximum profit if the firm's total costs are fixed at $100. Estimate the new optimal profit if total costs rise by 7%.

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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Solve by the method of Lagrange Multipliers: A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q, + 10Q2 where Q, and Q, denote the quantities of G1 and G2 respectively. If P, and P2 denote the corres- ponding prices then the demand equations are P = 50 – Q1 – Q2 P2 = 100 – Q, - 4Q2 Find the maximum profit if the firm's total costs are fixed at $100. Estimate the new optimal profit if total costs rise by 7%.
Transcribed Image Text:Solve by the method of Lagrange Multipliers: A monopolistic producer of two goods, G1 and G2, has a total cost function TC = 5Q, + 10Q2 where Q, and Q, denote the quantities of G1 and G2 respectively. If P, and P2 denote the corres- ponding prices then the demand equations are P = 50 – Q1 – Q2 P2 = 100 – Q, - 4Q2 Find the maximum profit if the firm's total costs are fixed at $100. Estimate the new optimal profit if total costs rise by 7%.
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