   Chapter 9.9, Problem 33E ### 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) Graph the marginal profit function for the profit function P ( x ) =   30 x   — x 2 — 200 , where P ( x ) is in thousands of dollars and x is hundreds of units.(b) What level of production and sales will give a 0 marginal profit?(c) At what level of production and sales will profit be at a maximum?(d) What is the maximum profit?

(a)

To determine

To graph: The marginal profit function for the profit function P(x)=30xx2200 where P(x) is in hundreds of dollars and x is hundreds of units.

Explanation

Given Information:

The provided profit function is P(x)=30xx2200 where P(x) is in hundreds of dollars and x is hundreds of units.

Graph:

Consider the provided profit function, P(x)=30xx2200

It is known that if P=P(x) is the profit function for a product, then the marginal profit function is MP¯=P(x).

So, if the profit function is P(x)=30xx2200, then the marginal profit function is,

P(x)=302x

Now, draw the graph of P(x)=302x by

Choose some values for x and compute the value for P(x), in order to form the ordered pairs.

Put x=0 in the function P(x)=302x.

P(x)=302x=302(0)=30

Now, put x=5 in the function P(x)=302x.

P(x)=302x=302(5)=3010=20

Now, put x=15 in the function P(x)=302x

(b)

To determine

To calculate: The level of production and sales that give a zero-marginal profit.

(c)

To determine

To calculate: The level of production and sales at which the profit will be maximum.

(d)

To determine

To calculate: The maximum profit for the profit function P(x)=30xx2200 where P(x) is in hundreds of dollars and x is hundreds of units.

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