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There are only two companies that produce running shoes: X and Y. The shoes they produce are similar but still slightly different from each other. The demand for shoes produced by X is given by Dx(Px,PY)-1000 - Px + 0.2(Px- PY), and the demand for shoes produced by Y is given by DY(Px,PY)%3D1000 – Py + 0.2( Py- Px). The cost of production is zero and each firm can produce any number of shoes between 0 and 1000. 3) How many shoes will each firm produce and what will be each firm's profit? 4) If the firms merge into one firm XY that can produce both types of shoes, how many of each type of shoes will XY produce and what will its profit be? As before, assume XY can produce any number between 0 and 1000 of each type of shoes.

There are only two companies that produce running shoes: X and Y. The shoes they produce are similar but still slightly different from each other. The demand for shoes produced by X is given by Dx(Px,PY)-1000 - Px + 0.2(Px- PY), and the demand for shoes produced by Y is given by DY(Px,PY)%3D1000 – Py + 0.2( Py- Px). The cost of production is zero and each firm can produce any number of shoes between 0 and 1000. 3) How many shoes will each firm produce and what will be each firm's profit? 4) If the firms merge into one firm XY that can produce both types of shoes, how many of each type of shoes will XY produce and what will its profit be? As before, assume XY can produce any number between 0 and 1000 of each type of shoes.

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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There are only two companies that produce running shoes: X and Y. The shoes they produce are similar but still slightly different from each other. The demand for shoes produced by X is given by Dx(Px,PY)=1000 - Px + 0.2(Px- PY), and the demand for shoes produced by Y is given by DY(Px,PY)=1000 – Py + 0.2( PY- Px). The cost of production is zero and each firm can produce any number of shoes between 0 and 1000. 3) How many shoes will each firm produce and what will be each firm's profit? 4) If the firms merge into one firm XY that can produce both types of shoes, how many of each type of shoes will XY produce and what will its profit be? As before, assume XY can produce any number between 0 and 1000 of each type of shoes.
Transcribed Image Text:There are only two companies that produce running shoes: X and Y. The shoes they produce are similar but still slightly different from each other. The demand for shoes produced by X is given by Dx(Px,PY)=1000 - Px + 0.2(Px- PY), and the demand for shoes produced by Y is given by DY(Px,PY)=1000 – Py + 0.2( PY- Px). The cost of production is zero and each firm can produce any number of shoes between 0 and 1000. 3) How many shoes will each firm produce and what will be each firm's profit? 4) If the firms merge into one firm XY that can produce both types of shoes, how many of each type of shoes will XY produce and what will its profit be? As before, assume XY can produce any number between 0 and 1000 of each type of shoes.
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