Why is the answer for b. the way it is

[yung]

A bus service that serves a local college campus has a standard fare of $4.50 per ticket and gives a reduction of $0.10 per ticket as an incentive for groups. The company estimates that it says $200.00 in gas plus overhead expenses of $2.00 per ticket.
a. Write a simplified polynomial function for the bus service’s total cost, C(x), where x is the number of tickets.
b. Write a simplified polynomial function for the bus service’s revenue.
c. Determine a profit function, P(x).
d. Determine an average profit (profit per ticket) function.


The answer for b. is: Revenue = R(x) 4.50x - 0.10x^2


why is it? how do you know how many of tickets are sold at full fare and how many are sold at reduced fare?

 

[skeeter]

let x = number in the group

revenue = (number of tickets sold)(normal price - discount)

R(x) = x(4.50 - .10x)

 

[yung]

thank you for your reply

I'm still a bit puzzeled

if only 1 ticket was sold x=1 then the answer is $4.40 (the discounted fare)

however if 1 ticket was sold then obviously there should not be any group discounts.

the answer implies all tickets sold has a discount, group or no group.

in that case shouldn't the answer be R(x) = 4.4x ?

perhaps I'm not understanding the question correctly

 

[skeeter]

Seems to me that a group has to be defined as a number greater than 1. Don't make it any harder by trying to nit-pick the problem's lack of a proper definition for the word "group". Let common sense guide you in this case.

 

[yung]

but what about if there are 45 people going on the bus? R(x) = x(4.5-0.1x) would make the revenue be zero? that just doesn't make any sense

 

[Deleted member 4993]

That is why this exercise is important.

The capacity of the bus should be less than 45 - in fact equal to 22 or 23. Otherwise don't set up such discount scheme.