Chapter 14.3, Problem 25E

### 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 p 1 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 23 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=3008p14p2 and q2=4005p110p2 are equal.

Explanation

Given Information:

The demand functions for the two products are given by q1=300âˆ’8p1âˆ’4p2 and q2=400âˆ’5p1âˆ’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=300âˆ’8p1âˆ’4p2 and q2=400âˆ’5p1âˆ’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=q2300âˆ’8p1âˆ’4p2=400âˆ’5p1âˆ’10p2âˆ’4p2+10p2=400âˆ’5p1âˆ’300+8p16p2=100+3p1

Divide both side of the equation 6p2=100+3p1 by 6.

6p26=100+3p16p2=1006+3p16p2=503+p12

Let p1=4

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