   Chapter 11.4, Problem 21E ### 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

# Capital investment and production Suppose that for a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested, with x =   30 y   +   20 y 2 . At what rate will production increase if $10,000 is invested and if the investment capital is increasing at a rate of$1000 per month?

To determine

To calculate: The rate of change of production if $10,000 is invested and the investment capital is increasing at a rate of$1000 per month if x=30y+20y2.

Explanation

Given Information:

For a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested with,

x=30y+20y2

The amount invested is $10,000 and investment capital is increasing at the rate of$1000 per month.

Formula used:

The derivative formula,

ddxxn=nxn1

Calculation:

As it is provided that for a particular product, the number of units x produced per month depends on the number of thousands of dollars y invested with,

x=30y+20y2

Now, the rate at which the production is changing will be obtained by differentiating the above equation with respect to t as,

dxdt=30dydt+

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