Two companies are producing widgets. It costs the first company q12 dollars to produce q1 widgets and the second company 0.5q22 dollars to produce q2 widgets. If a total of q widgets are produced, consumers will pay 200 - q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce? (The model for this type of problem is called a collusive duopoly model.)

Two companies are producing widgets. It costs the first company q12 dollars to produce q1 widgets and the second company 0.5q22 dollars to produce q2 widgets. If a total of q widgets are produced, consumers will pay 200 - q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce? (The model for this type of problem is called a collusive duopoly model.)

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section9.5: Multistage Decision Problems

Problem 19P

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Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

Two companies are producing widgets. It costs the first company q₁² dollars to produce q1 widgets and the second company 0.5q₂² dollars to produce q₂ widgets. If a total of q widgets are produced, consumers will pay 200 - q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce? (The model for this type of problem is called a collusive duopoly model.)

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