Explanation Given information: When the price of the product is $25, the company sells 500 units per week. When the price of the product is $30, the number of sold per week decreases to 460 units. Formula used: The demand q is given by the formula q = k p + l . Where, q is the demand and p is price per unit. Calculation: When the price of the product is $25, the company sells 500 units per week. ⇒ q 1 = 500 , p 1 = 25 Then the demand q = k p + l is given by 500 = 25 k + l (1) When the price of the product is $30, the number of sold per week decreases to 460 units. ⇒ q 2 = 460 , p 2 = 30 Then the demand q = k p + l is given by 460 = 30 k + l (2) ( 1 To determine (b) To find: The revenue function of price if the demand q = − 8 p + 700. To determine (c) To graph: The revenue function R = 700 p − 8 p 2 and to find the price that maximizes the revenue and the value of revenue at that price.

6th Edition

ISBN: 9781119275565

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 1.9, Problem 28P

To determine

(a)

To find:

The demand, q, as a function of price, p, assuming that the demand curve is linear.

To determine

(b)

To find:

The revenue function of price if the demand q=−8p+700.

To determine

(c)

To graph:

The revenue function R=700p−8p2 and to find the price that maximizes the revenue and the value of revenue at that price.

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Chapter 1.9, Problem 27P

Chapter 1.9, Problem 29P

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Chapter 1 Solutions

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(a) To find: The demand, q, as a function of price, p, assuming that the demand curve is linear.

Solution Summary: The author calculates the demand q as a function of price, p, using the formula q=kp+l. When the price is 25, the company sells 500 units per week.

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(a) To find: The demand, q, as a function of price, p, assuming that the demand curve is linear.

(b) To find: The revenue function of price if the demand q=−8p+700.

(c) To graph: The revenue function R=700p−8p2 and to find the price that maximizes the revenue and the value of revenue at that price.

Want to see the full answer?

Chapter 1 Solutions

(a)

To find:

The demand, q, as a function of price, p, assuming that the demand curve is linear.

(b)

To find:

The revenue function of price if the demand q=−8p+700.

(c)

To graph:

The revenue function R=700p−8p2 and to find the price that maximizes the revenue and the value of revenue at that price.