# If the capacity of the bus system is 5000 passengers, what should the bus system charge to produce the largest possible revenue in the following case:A city bus system carries 4000 passengers a day...

If the capacity of the bus system is 5000 passengers, what should the bus system charge to produce the largest possible revenue in the following case:

A city bus system carries 4000 passengers a day throughout a large city. The cost to ride the bus is \$1.50/person. The owner realizes that 100 fewer people would ride the bus for each \$0.25 increase in fare, and 100 more people would ride for each \$0.25 decrease in fare.

Asked on by agent09

### 3 Answers |Add Yours

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

With a fare of \$1.5 there are 4000 passengers of the bus service.

A \$0.25 increase in fare decreases the number of passengers by 100 and a \$0.25 decrease in fare increases the number of passengers by 100.

For a change in the fare of x, the total revenue

R = (4000 - 100*x)(1.5 + x*0.25)

=> 6000 - 150x + 1000x - 25x^2

To maximize R, solve R' = 0

R' = -150 + 1000 - 50x

-150 + 1000 - 50x = 0

=> 50x = 850

=> x = 17

The price of ticket should be increased by \$4.25 to \$5.75

Revenue is maximized when the fare is increased to \$5.75.

agent09 | Student, Undergraduate | (Level 2) eNoter

Posted on

I do not think it is the right way to approach this question :( So far I have worked this

`P(c)= 4000-(c-1.50)(100/0.25)`

`=4000-400c+600`

`=4600-400c`

I don't know what to do after this. Anyone would like to help me please, I have a test tomorrow and my teacher said questions like this will be on the test.

charlierocks14 | Student, Grade 10 | (Level 1) Honors

Posted on

Ok, begin by calculating how much the bus system makes each day.  4000x\$1.50=\$6000

Now, think about how much the 100 fewer people would cost the company.

3900x\$1.50=\$5850, which is a 150 dollar decrease

And the company would make \$.25 more per passenger so...

3900x\$1.75=\$6825

Then calculate the same thing for the other scenario.

4100x\$1.50=\$6150

and,

4100x\$1.25=\$5125

As you can see, the \$.25 increase is better for the company in the long run.  So the bus system should charge \$1.75 for bus fare to make the largest possible revenue.

We’ve answered 317,747 questions. We can answer yours, too.