SOLUTION: Please help me with this question (its a max/min problem): It costs a bus company $225 to run a minibus on a ski trip, plus $40 per passenger. The bus has seating for 22 passeng

Question 926947: Please help me with this question (its a max/min problem):
It costs a bus company $225 to run a minibus on a ski trip, plus $40 per passenger. The bus has seating for 22 passengers, and the company charges $60 per fair if the bus is full. For each empty seat, the company has to increase the ticket price by $5. How many empty seats should the bus run with to maximize profit?
I know to find profit it is revenue minus the cost, and cost is 225 + 40x
and i think revenue is (22 + x)(60 + 5x)
so i subtracted those: [(22 + x)(60 + 5x)] - (225 + 40x)
but when i completed the square i got a negative number. please help

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
It costs a bus company $225 to run a minibus on a ski trip, plus $40 per passenger.
The bus has seating for 22 passengers, and the company charges $60 per fair if the bus is full.
For each empty seat, the company has to increase the ticket price by $5. How many empty seats should the bus run with to maximize profit?
:
If x = no. of empty seats,then it should be:
revenue is (22 - x)(60 + 5x) = 1320 + 110x - 60x - 5x^2
then: f(x) = [-5x^2 + 50x + 1320] - (225 + 40x)
f(x) = -5x^2 + 50x + 1320 - 225 - 40x
f(x) = -5x^2 + 10x + 1095
The axis of symmetry will be the max x
x =
x = 1 empty seat would give max profit ($1100)
RELATED QUESTIONS
Hi, Would you please be able to help me. I need to understand the formula to add into a... (answered by stanbon)

Hi, Would you please be able to help me. I need to understand the formula to add into a... (answered by Theo,solver91311)

I hope you can help me. I am having a little trouble with this word problem. " A ski... (answered by checkley71)

I have been struggling on this problem for awhile now and I was wondering if someone... (answered by ankor@dixie-net.com)

I have been working on this problem and I have tried it many times and I still can't... (answered by ankor@dixie-net.com)

Please help me answer this question, thanks(: The price per person of renting a bus... (answered by ankor@dixie-net.com)

A ship must average 22 miles per hour to make its ten hour run on schedule. During the... (answered by checkley71)

Please help me answer this problem, thanks. The price per person of renting a bus... (answered by ankor@dixie-net.com)

Please help me with this question. Max earned an 88% on a exam with 25 problems. How... (answered by mouk)