26. The price, p, in dollars and the quantity demanded, x,...

26. The price, p, in dollars and the quantity demanded, x, for World Cup tickets are related by the equation $x = 900 - 25p$ a) Solve for the price, p Answer: b) Find the revenue function, $R(x)$, from the sale of x tickets. Answer: c) Find the marginal revenue function. Answer:

Transcript

00:01 Hey, so for problem 39, we're given a word problem, and we have to find the total revenue function if the revenue from 100 t -shirts is 10 ,000.

00:14 So over here we have an equation for our prime of x, and the prime indicates that it would be the derivative.

00:23 So to find the r of x, which is what we need, we're going to take the integral of this.

00:32 So the integral of this equation.

00:48 So to do this we're going to use you substitution and substitute whatever's inside the parentheses and replace that with you.

00:59 So we're going to set you equal x squared plus 17 ,000.

01:07 So if you take the derivative of both sides you get du equals 2x dx and we can go ahead and move the 2 to the other side.

01:19 So it would be du over 2 equals x dx.

01:31 And as you can see up here, we have an x.

01:37 So we can go ahead, and i'm missing a dx over here.

01:44 So we can go ahead and substitute all of our points.

01:52 So here we're going to make the substitution.

01:55 This equals the integral of u to the negative two -thirds times the green circles which are d u over two and we also have a lone five here so we have to include that times five and we can move the constants to the front so the constant in this case is five over two so we can move that in front of the integral and we have the integral of you to the negative two thirds du.

02:34 And if you solve this, you get you add 3 over 3, so it would be u to the 1 3 times 3, then bring down the 5 over 2, and then plus c.

02:54 We need the plus c because it's an indefinite integral, it has no bounds.

03:00 And now you can simplify this, and that would be 15 over 2 and you have to plug in the u back into the equation since we can't have u as part of the answer it would be if you plug in this into u you get a c and just remember that this we were solving for x r of x and the question asks us to find the total revenue function if the revenue from 100 t -shirt is $10 ,000.

03:50 So in this case we would have to plug in 100 for x.

03:57 So you plug in 100 for x.

04:02 So if you do that and rfx would be 10 ,000, we can go ahead and do that on a separate page.

04:30 So i went ahead and just copied this last step over here and put it on a separate page...

Question

26. The price, p, in dollars and the quantity demanded, x, for World Cup tickets are related by the equation $x = 900 - 25p$ a) Solve for the price, p Answer: b) Find the revenue function, $R(x)$, from the sale of x tickets. Answer: c) Find the marginal revenue function. Answer:

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