   Chapter 11.4, Problem 81E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Marginal Profit Paramount Electronics has an annual profit given by P = − 100 , 000 + 5 , 000 q − 0.25 q 2  dollers, where q is the number of laptop computers it sells each year. The number of laptop computers it can make and sell each year depends on the number n of electrical engineers Paramount employs, according to the equation q = 30 n + 0.01 n 2 . Use the chain rule to find d P d n | n = 10 andinterpret the result. [HINT: See Example 4.]

To determine

To calculate: The value of dPdn|n=10 if it is given that paramount electronics has an annual profit given by the equation P=100,000+5,000q0.25q2dollars where q is the number of laptops and computers sold each year and the number of laptop computers sold each year depends on the number n of electrical engineers paramount employs given by the function q=30n+0.01n2.

Explanation

Given Information:

Paramount electronics has an annual profit given by P=100,000+5,000q0.25q2dollars where q is the number of laptops and computers sold each year and the number of laptop computers sold each year depends on the number n of electrical engineers paramount employs given by the function q=30n+0.01n2.

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x.

Calculation:

Consider the function, P=100,000+5,000q0.25q2

So,

dPdq=ddq(100,000+5,000q0.25q2)=5,0000.25(2)q=5,0000.5q

Also consider the function, q=30n+0.01n2

dqdn=ddn(30n+0.01n2)=30+0.02n

The two derivatives are:

dPdq=5,0000

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