The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping the bus fare as part of a promotion to increase the ridership on that route. Lately, the busses have only been at half capapcity. The bus company's research shows that for every $5 decrease they will gain 2 more riders.

a) define variables and set up an equation to represent this scenario

b) What is the maximum revenue the bus company can earn and what will be the cost of a ticket when the revenue is at a maximum

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yogeshkumar49685 yogeshkumar49685 · Answer 1 · 2022-08-04T18:48:04+02:00

If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6

Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.

We are required to find the maximum revenue that the bus company can earn.

Suppose x represents the number of seats, y represents the total amount.

Price=$156

Seats=56

When the bus is of half capacity the bus seats will be 28.

As price decreases th rider gains 2 more.

Revenue equation.

y=(156.5x)(28+2x)-------------1

Expanding the equation.

y=4368-140x+312-10[tex]x^{2}[/tex]

Differentiating with respect to x.

dy/dx=0-140+312-20x

=172-20x

Put dy/dx=0

172-20x=0

x=8.6

Substitute the value of variable x in the equation 1.

y=(156-5x)(28+2x)

=$5107.6

Hence the maximum revenue that the bus company can earn is $5107.6.

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