   Chapter 4.6, Problem 45E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
115 views

# Revenue A small business assumes that the demand function for one of its new products can be modeled by p = C e k x When p = $45, x = 1000 units, and when p =$40, x = 1200 units.(a) Solve for C and k in the model.(b) Find the values of x and p that will maximize the revenue for this product.

(a)

To determine

To calculate: The value of C and k in the demand model p=Cekx of a small business company, when p=$45, x=1000 units and when p=$40, x=1200 units

Explanation

Given Information:

The provided demand model is p=Cekx and values of p, x are p=$45, x=1000 units and p=$40, x=1200 units.

Calculation:

Consider the demand equation p=Cekx and the values of p, x are p=$45, x=1000 units and p=$40, x=1200 units.

First, substitute p=$45, x=1000 units in the equation p=Cekx. 45=Cek(1000)45=Ce1000k Now, substitute p=$40, x=1200 units in the equation p=Cekx.

40=Cek(1200)40=Ce1200k

Now, take ration of the equations Ce1200k=40, Ce1000k=45 as,

Ce1200kCe1000k=4045e1200k1000k=89e200k=89

Take natural log on both the sides,

ln(e200k<

(b)

To determine

To calculate: The values of x and p that will maximize the revenue of a small business company with demand model p=Cekx, when p=$45, x=1000 units and when p=$40, x=1200 units.

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