   Chapter 11.4, Problem 18E ### 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

# Profit Suppose that the monthly revenue and cost (in dollars) for x units of a product are R =   400 x   −   x 2 20  and  C   =   5000   + 70 x At what rate per month is the profit changing if the number of units produced and sold is 200 and is increasing at a rate of 5 units per month?

To determine

To calculate: The rate per month at which the profit is changingwhen the number of units produced and sold is 200 and is increasing at a rate of 5 units per day if R=400xx220 and C=5000+70x.

Explanation

Given Information:

The monthly revenue and cost (in dollars) for x units of a product are,

R=400xx220

And,

C=5000+70x.

Number of units produced and sold is 200 and is increasing at a rate of 5 units per day.

Formula used:

The derivative formula,

ddxxn=nxn1

Calculation:

As it is provided that the monthly revenue and cost (in dollars) for x units of a product are,

R=400xx220

And,

C=5000+70x.

Now, profit is the difference of revenue and cost, thus,

P=RC=400xx220500070x=330xx2205000<

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