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Suppose the demand equation is $p=\sqrt{2000-5 x}$, where $x$ is the number of items sold when the per unit price is $p$ dollars. Determine (a) the revenue function, (b) the domain revenue function, (c) the revenue derived from the sale of the 100 th item $-$ the marginal revenue when $x=100,$ (d) estimate the level of production that maximizes the revenue, and the maximum revenue.

(a) $R(x)=x \sqrt{2000-5 x}$(b) $0 \leq x \leq 400$(c) 35.73(d) 267,11940

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Missouri State University

University of Michigan - Ann Arbor

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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Suppose the demand equatio…

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Suppose it has been determ…

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Suppose the demand equati…

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Demand function, $p=D(x),$…

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The price $p$ (in dollars)…

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Demand Equation The demand…

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The price $p,$ in dollars,…

So let's suppose that the demand function um is the equation P equals Square root of 2000 -5 x. Our X. Is the number of items sold and p is the unit price in dollars. So we want to determine the revenue function and the domain revenue function. So uh the revenue function, our events is just equal to X times the demand functions. We're just gonna have this right here. Let me see. The domain of this function is going to be 400 Then or from 0 to 400 times. And then we have the revenue derived from the sale of the 100 item, Which is the marginal revenue when x equals 100. So the marginal revenue is going to be our crime Of 100 and which is at that price is going to be 32 dollars. Yeah. Um And then the production level of production, we can also maximize the revenue. What Tracy to maximize revenue is right here.

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