   Chapter 10.3, Problem 42E ### 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

# A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars, given by C ¯ = 800 x 100 x + x 2 The daily demand for x units of its product is given by p =   60 , 000   −   50 x dollars. Find the quantity that gives maximum profit and find the maximum profit. What selling price should the corporation set for its product?

To determine

To calculate: The quantity that gives maximum profit and find the maximum profit and the selling price should the corporation set for is product if the daily demand for x units product is given by p=60,00050x.

Explanation

Given information:

The large corporation with monopolistic control in the marketplace has its average daily costs, in dollars given by:

C¯=800x+100x+x2

The daily demand for x units product is given by:

p=60,00050x

Formula used:

The total profit function is:

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

Where R(x)&C(x) are total revenue function and total cost function.

Calculation:

Consider the provided information:

The daily demand for x units product is given by p=60,00050x.

The large corporation with monopolistic control in the marketplace has its average daily costs, in dollars given by:

C¯=800x+100x+x2

R(x) can be defined as:

R(x)=px=60,000x50x2

C(x) can be defined as:

C(x)=C¯x=800+100x2+x3

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)=60,000x50x2(800+100x2+x

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