A bus company charges $15 per person for the first 50 passengers who buy tickets for a gold outing. The company offers a discount of $0.10 per ticket for each passenger in excess of 50. What number of passengers will provide maximum income for the bus company ?

Question

A bus company charges $15 per person for the first  50 passengers who buy tickets for a gold outing. The company offers a discount of  $0.10 per ticket for each passenger in excess of 50. What number of passengers will provide maximum income for the bus company ?

jabez177 · Answer

Ehhhh... It's been a while since I've seen these questions.

jabez177 · Answer

@pooja195 @Luigi0210 @hartnn

jeanfifa09 · Answer

I need help doing it , I'm a little bit stuck

shaik0124 · Answer

what have u done so far

shaik0124 · Answer

for first 50 passengers ticket cost will be $15 
then from 51st passenget onwards the ticket cost will be $14.9

jeanfifa09 · Answer

I need to find the number of passengers that will provide maximum income for the bus company

jeanfifa09 · Answer

This is an optimization problem ,for calc 1

ganeshie8 · Answer

is the complete statement of the problem ?

jeanfifa09 · Answer

I have 
I = # of passengers * price per passengers 
I = (50+x)(10-.10x)
I = 500-5x+10x-0.1x^2
Do I take the derivative ? I'm stuck right there ,

jeanfifa09 · Answer

That is the complete statement .

jeanfifa09 · Answer

What do you mean by complete statement ?

jeanfifa09 · Answer

I meant to write above 
I = (50+x)(15-0.1x)

miracrown · Answer

yes - we need derivatives now, what is the derivative of this function?

jeanfifa09 · Answer

dI/dx=10-0.2X

miracrown · Answer

Sorry, my connection was acting fuzzy. So yes if you want to optimize you need to derive and make this equal to 0

jeanfifa09 · Answer

0=10-0.2x   ?
0.2x=10   
X= 50   ?

miracrown · Answer

Let me show you:
dI/dx= 5-(0.1)(2)x

miracrown · Answer

I = 500-5x+10x-0.1x^2 =5x-(0.1)(2)x

miracrown · Answer

you see?

miracrown · Answer

So this new one, could you equal it to 0 and find the x?

jeanfifa09 · Answer

I made a mistake originally , I fixed it to be : 

I= (50+x)(15-0.10x) 
Which equals to 
I = 750+10x-0.1x^2

I wrote (50+x)(10-0.10x) which was wrong . The price is $15 not $10

miracrown · Answer

Oh, ok. So the derivative would be?

jeanfifa09 · Answer

The derrative of that would be 
dI/dx= 10-0.2X

miracrown · Answer

Yep! So when its equal to zero?

jeanfifa09 · Answer

0=10-.2x
.2x=10
X=50?

miracrown · Answer

Yess!!!

miracrown · Answer

so at 50 persons the price get to its maximum :)

jeanfifa09 · Answer

After what do I do next ? Plug it in the original equation ?

miracrown · Answer

Nope! That's your answer X = 50 !

jeanfifa09 · Answer

Oh ok

jeanfifa09 · Answer

Thank you so much!!!

miracrown · Answer

You're most welcome! Good luck with your studies! :D