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Suppose the demand equation is $200 x+10 p=10000,$ where $x$ is the number of items sold when the per unit price is $p$ dollars. Determine (a) the revenue function, (b) the domain of the revenue function, (c) the revenue derived from the sale of the 20 th item - the marginal revenue when $x=20$, (d) the level of production that maximizes the revenue, and the maximum revenue.

(a) $R=-20 x^{2}+1000 x$(b) $0 \leq x \leq 50$(c) $\$ 220$(d) $25, \$ 12,500$

Algebra

Chapter 1

Functions and their Applications

Section 6

Economic Functions

Functions

Missouri State University

Harvey Mudd College

Idaho State 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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Suppose the demand equati…

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Suppose the demand equatio…

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Suppose it has been determ…

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The price $p$ (in dollars)…

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The price p (in dollars) a…

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Maximizing Revenue The pri…

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Demand Equation The demand…

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A price function, $p$, is …

for the problem given to us here we have a demand function of 200 X plus 10. P. Equals 1000. Mhm. And and we want to uh you know access the number right and sold and P. Is the price of dollars. So let's determine the revenue function. In order to do that. Let's first get our key function. So we're gonna subtract 200. Excellent. And then divided by 10. That makes this negative 20 X plus 100. And we know that our revenue function, our vets is going to be X. Times the demand function. So we'll get a negative 20 X. Squared Plus 100 x. And we see that the domain is going to be from 0-5. Um And then This was 10,000. So this needs to be 1000. This will be 1000. So it's actually me 50 is the domain 0-50. Um and then we see that the revenue derived from the sale of the 20th item. So we would have our 20, I'd be 12,000. We can also look at marginal revenue and all these other important economic functions

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