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Suppose it has been determined that the demand (in thousands of dollars) for a certain item is given by the equation $p=\frac{20}{\sqrt{x}}$ and the cost of producing $x$ hundred items is given by $C(x)=5 x+10 .$ Determine (a) the revenue function, (b) the Profit function, (c) estimate the level of production $x$, at which profit will be maximized, (d) from your estimate in (c), what price should be charged to maximize profit?

(a) $R(x)=20 \sqrt{x}$(b) $P(x)=20 \sqrt{x}-5 x-10$(c) 4(d) 10

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Oregon State University

Harvey Mudd College

Baylor University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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01:16

Suppose the demand equatio…

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01:12

Profit The demand function…

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Maximizing Revenue The pri…

12:36

The price $p$ (in dollars)…

05:11

So let's suppose it's been determined that the demand in thousands of dollars of a certain for a certain time Is given by the equation 20 overruled x. p. equals 20 overrode x. I'm in the cost of producing X00 items would be given by CFX is equal to hi that Carson. So then we want to determine the revenue function, the profit function. Um So the revenue function is going to be okay X times the profit function or the demand function, that's gonna be 20 x over DX. And then the profit function is going to equal the revenue function minus the cost function. So that's why I end up giving us all the functions we need to solve the problem.

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