Chapter 14.3, Problem 26E

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 23-26, prices q 2 and p 2 are in dollars and q 1 and q 2 are numbers of units.Find a pair of prices p 1  and  p 2 such that the demands for the two products in Problem 24 will be equal.

To determine

To calculate: A pair of prices p1 and p2 such that the demands for the two products given by q1=9009p1+2p2 and q2=1200+6p110p2 are equal.

Explanation

Given Information:

The demand functions for the two products are given by q1=900âˆ’9p1+2p2 and q2=1200+6p1âˆ’10p2.

Formula used:

To find a pair of a solution (x,y) such that the two functions f(x,y) and g(x,y) are equal, set f=g.

Calculation:

The demand functions for the two products are given by q1=900âˆ’9p1+2p2 and q2=1200+6p1âˆ’10p2.

Thus, q1 and q2 represents the demand for the two products. Also, p1 and p2 represents the prices of the two products.

Recall that, to find a pair of a solution (x,y) such that the two functions f(x,y) and g(x,y) are equal, set f=g.

Set q1=q2, so that the two demand functions are equal.

q1=q2900âˆ’9p1+2p2=1200+6p1âˆ’10p22p2+10p2=1200+6p1âˆ’900+9p112p2=300+15p1

Divide both sides of the above equation 12p2=300+15p1 by 12

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