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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Revenue Repeat Exercise 45 given that when   p = $5,  x  -300 units, and when  p  = $4,  x = 400 units .

(a)

To determine

To calculate: The value of C and k in the demand model p=Cekx of a small business company, when p=$5, x=300 units and when p=$4, x=400 units.

Explanation

Given Information:

The provided demand model is p=Cekx and values of p, x are p=$5, x=300 units and when p=$4, x=400 units.

Calculation:

Consider the demand equation p=Cekx and the values of p, x are p=$5, x=300 units and when p=$4, x=400 units.

First, substitute p=$5, x=300 units in the equation p=Cekx.

5=Cek(300)5=Ce300k

Now, substitute p=$4, x=400 units in the equation p=Cekx.

4=Cek(400)4=Ce400k

Now, take ration of the equations Ce400k=4, Ce300k=5 as,

Ce400kCe300k=45e400k300k=45e100k=45

Take natural log on both the sides,

ln(e100k

(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=$5, x=300 units and when p=$4, x=400 units.

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