Question

A company that conducts bus tours that when the price was $9.00 per person, the average number of customers was 1000 per week. When the company reduced the price to $7.00 per person, the average number of costumers increased to 1500 per week. Assuming that the demand function is linear, what price should be charged to obtain the greatest weekly revenue? Revenue is price times number sold. Also find this maximum revenue.

Answer 1

What math class is this for?

Answer 2

I need to know so that I explain how to solve this with methods you know.

Answer 3

This is calculus math 251.

Answer 4

Okay then. I asked because this looked like Algebra 1 or 2.
Give me a few minutes to come up with a solution.

Answer 5

Okay thanks man :)

Answer 6

I dont know...I've never done this before :P My friend gave me this because I had tooken calculus before but a lot of it I have forgotten and I told him I would solve it for him. But like I have had no luck :/

Answer 7

Hmm. This isn't calculus. This is simple algebra.

Answer 8

This came out of a calculus math 251 book. So yeah Idk :P

Answer 9

That's fine then. I can still explain how to do this.

Answer 10

Hes taking a calculus class and he said his professor gave him this problem so yeah.

Answer 11

Okay awesome thanks :)

Answer 12

Do you know how to find the slope of two points?

Answer 13

So the function I get is y=(-x/250)+13

Answer 14

revenue is r=xy

Answer 15

And by maximizing the function, you want to find the vertex

Answer 16

The vertex is at 1625, (21125/2)

Answer 17

Isnt it D=squrt(x2-x1)+(y2-y1)?

Answer 18

yes

Answer 19

Well, kinda the opposite

Answer 20

y2-y1/(x2-x1)

Answer 21

Ohh okay yeah now I remember for the slope :P I was doing the distance :P

Answer 22

So now would I take the derivative of r?

Answer 23

yes

Answer 24

So basically like Chain Rule then :)

Answer 25

But you don't need to because you've already got everthing you needed.

Answer 26

The max revenue occurs at the vertex which is at (1625, 10562.5)

Answer 27

When there is 1625 people

Answer 28

Okay cool :) But what should the price be per person for maximum revenue?

Answer 29

6.50

Answer 30

Using the following function y = -x/250 + 13

Answer 31

I plugged in that number of customers to the demand function to obtain the corresponding price.

Answer 32

Does that makes sense?

Answer 33

Wait, one sec. that is not right.

Answer 34

So 6.5*1625

Answer 35

10562.5 would be max profit

Answer 36

Yeah thats the max revenue. And it should cost $6.50 per person. Correct?

Answer 37

yes

Answer 38

Okay how did you get the vertext? I know using the slope formula but what values did you use to replace them?

Answer 39

I used -b/2a

Answer 40

Where did you get that from?

Answer 41

Do you know how to find the vertex of a function?

Answer 42

Kinda sorta :P

Answer 43

Lol nvm I can solve the rest :) Thanks man :) I have to go so Ciao :D

Answer 44

ok