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Find the maximum revenue if the demand equation is: (a) $p=100 /(x+1)$(b) $p=\frac{\left(50-x^{4}\right)}{(x+2)} ;$ (c) $p+x=75 ;$ (d) $p^{2}+x^{2}=100$(e) $p^{2}-x=100 ;(\mathrm{f}) p^{2}+x^{2}=50$

(a) No max(b) 33.60(c) 1406.25(d) 50(e) not a demand equation(f) 25

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 5

Applications II - Business and Economic Optimization Problems

Derivatives

Oregon State University

Baylor University

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

03:12

Maximizing Revenue The pri…

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The price $p$ (in dollars)…

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04:04

01:22

Suppose the demand equatio…

02:46

Maximizing Revenue The dem…

02:17

Find $p_{1}$ and $p_{2}$ s…

you're demanding question between price and quantity. It's given that is equal toe minus off X by six plus 100. And in first part we have to find you a new ed Functional X. So we know that the venue is equal to price multiplied to it Quantity. So here price be multiplied with quantity. Sorry. When you will be minus off XY squared by six less 100 times Knicks Now In second part we have to find domain off the venue. We know that even you cannot be negative. So every venue are will be greater than equal to Jiro. But you can right minus off actually square by six plus 100 times X will be greater than equal toe Jiro. So from here we can write actually square by six is less than equal toe 100 x and from here actually be less 10 equal to 600. No, we know that one did He cannot be negative. X will be greater than equal toe judo. No entire part. We have to find the venue If 200 units are sold the venue for 2200 that will be minus hold 200 square the right by six plus 100 times 200 on solving this expression, we will get a very venue That will be Dola 13,000 333 point Basically now in fourth part we have to find quantity. It's maximize the venue. And what is the maximum revenge to maximize this re venue? Really? You'd the friend. She'll method own difference here. This br by DX will be equal to my Nestle's two x by six less 100. Now we will differentiate again. This equation then in the square be weighed by he exits Grant that will be equal to minus off one by three which is left Kenjiro From here we can say that this will lose less 10 0 From here we will get maximum now To get Maxima, we will put the outer by D X equals Kojiro. From here we will write Jiro equal to minus off two x by six plus under from here, will you next will be equal to 300 now for 300 quantity, we will get our maximum. But even the maximum re venue are will be equal to my Nestle 300 square Be right by six less 100 multiplied with 300 on solving this express and we will get it even read dollar 15 told you. But this is our maximum re venue now. In last part we have to find Christ. Would the company's all to maximize revenge? That means for maximums the venue What will be the price priced for maximum revenge will be minus ALS X by six you hear x will be equal to 300 be wide by six bless 100. This will be minus or 50 plus 100 that will be equal to $50.

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