   Chapter 10.3, Problem 41E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# An industry with a monopoly on a product has its average weekly costs, in dollars, given by C ¯ = 10 , 000 x 60 − 0.03 x + 0.00001 x 2 The weekly demand for x units of the product is given by p =   120   −   0.015 x dollars. Find the price the industry should set and the number of units it should produce to obtain maximum profit. Find the maximum profit.

To determine

To calculate: The price for that industry should set and the number of units industry should produce to obtain maximum profit moreover the maximum profit if the weekly demand for x units of the product is given by p=1200.015x dollars.

Explanation

Given information:

An industry with a monopoly on a product has its average weekly costs, in dollars, given by:

C¯=10,000x+600.03x+0.00001x2

The weekly demand for x units of the product is given by:

p=1200.015x dollars.

Formula used:

The formula to find revenue function,

R(x)=px

Where x is quality sold and p is market equilibrium price for the product.

Calculation:

Consider the provided information:

The weekly demand for x units of the product is given by p=1200.015x dollars.

An industry with a monopoly on a product has its average weekly costs, in dollars, given by:

C¯=10,000x+600.03x+0.00001x2

The R(x) can be defined as:

R(x)=px=120x0.015x2

The C(x) can be defined as:

C(x)=C¯(x)=10,000+60x0.03x2+0.00001x3

Now find out the value of P(x) as:

P(x)=R(x)C(x)

Now substitute the value of R(x) and C(x) as:

P(x)=120x0.015x2(10,000+60x0.03x2+0.00001x3)=10,000+60x+0

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