A monopolist produces three products: A, B, and C. The demand functions for these three products...
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A monopolist produces three products: A, B, and C. The demand functions for these three products are given by: QA = 20-PA QB = 12 - PB 28 3 Imagine that producing one unit of the product A requires twice the input needed to produce one unit of product B while it re- quires three times the input needed to produce one units of prod- uct C. The monopolist could produce 1,000 units of product A per week if it only produces product A. Qc= = - Pc (a) Write down the optimisation question to find the values of 2A, QB. and Qc that will maximise the weekly revenue of the monopolist. [3 points] (b) Find the optimal values of Q, Q. and that maximise the weekly revenue of the monopolist using the Lagrange method. [12 points] (c) What's the interpretation of the Lagrange multiplier in this case? Please be concise and express in your own words. [3 points] A monopolist produces three products: A, B, and C. The demand functions for these three products are given by: QA = 20-PA QB = 12 - PB 28 3 Imagine that producing one unit of the product A requires twice the input needed to produce one unit of product B while it re- quires three times the input needed to produce one units of prod- uct C. The monopolist could produce 1,000 units of product A per week if it only produces product A. Qc= = - Pc (a) Write down the optimisation question to find the values of 2A, QB. and Qc that will maximise the weekly revenue of the monopolist. [3 points] (b) Find the optimal values of Q, Q. and that maximise the weekly revenue of the monopolist using the Lagrange method. [12 points] (c) What's the interpretation of the Lagrange multiplier in this case? Please be concise and express in your own words. [3 points]
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The image contains a problem statement that sets up an optimization scenario for a monopolist producing three different products labeled A B and C each with its own demand function Additionally it des... View the full answer
Related Book For
Operations management processes and supply chain
ISBN: 978-0136065760
9th edition
Authors: Lee J Krajewski, Larry P Ritzman, Manoj K Malhotra
Posted Date:
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