   Chapter 12.2, Problem 47E ### 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

# Physical productivity The total physical output of a number of machines or workers is called physical productivity and is a function of the number of machines or workers. If P = f ( x ) is the productivity, dP/dx is the marginal physical productivity. If the marginal physical productivity for bricklayers is d P / d x   = 90 ( x +   1   ) 2 , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 4 bricklayers. ( N o t e :   P   = 0   w h e n   x =   0. )

To determine

To calculate: The physical productivity of 4 bricklayers if marginal physical productivity for bricklayers is dPdx=90(x+1)2.

Explanation

Given Information:

The marginal physical productivity for bricklayers is,

dPdx=90(x+1)2

Where P the number of bricks is laid per day and x is the number of bricklayers.

And, for x=0,P=0.

Formula used:

The power rule of integral,

xndx=xn+1n+1+C

Calculation:

As it is provided that the marginal physical productivity for bricklayers is,

dPdx=90(x+1)2

Where P the number of bricks is laid per day and x is the number of bricklayers.

Now, the marginal physical productivity can be obtained by differentiating the physical productivity function as,

P(x)=90(x+1)2

Thus, the physical productivity can be obtained by integrating the above function as,

P(x)=90(x+1)2dx

Now, integrate the above function using power rule of integrals as,

P(x)=

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