   Chapter 11, Problem 12T ### 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

# Suppose the weekly revenue and weekly cost (both in dollars) for a product are given by R ( x ) =   300 x −   0.001 x 2  and  C ( x )   = 4000   +   30 x , respectively, where x is the number of units produced and sold. Find the rate at which profit is changing with respect to time when the number of units produced and sold is 50 and is increasing at a rate of 5 units per week

To determine

To calculate: The rate at which profit is changing with respect to time when the number of units produced and sold is 50 and is increasing at a rate of 5 units per week if suppose the weekly revenue and cost are given by R(x)=300x0.001x2 and C(x)=4000+30x, where x is the number of units produced and sold.

Explanation

Given Information:

The provided equations are R(x)=300x0.001x2 and C(x)=4000+30x.

Formula Used:

Power rule of derivative:

ddx(xn)=nxn1

Calculation:

The provided equations are R(x)=300x0.001x2 and C(x)=4000+30x,

The total profit is equal to:

P(x)=R(x)C(x)=0.001x2+300x30x4000=0.001x2+270x4000

Mow differentiate the above function with respect to t

ddt(P)=ddt(0.001x2+270x4000)=ddt(0.001x2)+ddt(270x)ddt(4000)

Now apply power rule of derivative:

ddt(0

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