   Chapter 9, Problem 94RE Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Revenue In a 100-unit apartment building when the price charged per apartment rental is ( 830   +   30 x ) dollars, the number of apartments rented is 100  - x and the total revenue for the building is R ( x ) = ( 830 + 30 x ) ( 100 − x ) where x is the number of $30 rent increases (and the resulting number of unrented apartments). Find the marginal revenue when x = 10 . Does this tell you that the rent should be raised (causing more vacancies) or lowered? Explain. To determine To calculate: The marginal revenue at x=10 with revenue function, R=(830+30x)(100x) and state whether the rent raised or lowered. Explanation Given Information: The revenue function of the commodity is R=(830+30x)(100x) and the$30 rent increases.

Formula used:

The simple power rule for the derivative,

ddx(xn)=nxn1

The rule of derivative for constant multiplication,

ddx[kf(x)]=kddx[f(x)]

The product rule of the derivative,

ddx[f(x)g(x)]=g(x)ddx[f(x)]+f(x)ddx[g(x)]

Calculation:

Consider the provided cost function, R=(830+30x)(100x)

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