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The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping this bus fare as part of a promotion to increase the ridership on that route.

The buses has only been at half capacity lately. The companies research shows that for every 5$ decreases they will gain 2 more riders.


1. Define variable and set up an equation to represent his scenario


2. 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

Respuesta :

MrRoyal

The bus tickets and price are illustrations of a quadratic function, and the maximum revenue the bus company can earn is $5107.6

The variables of the scenario

The variable representation used in this scenario are:

  • Let x represents the number of seats
  • Let y represents the total amount

The maximum revenue

The price is given as:

Price = $156

The number of seats is given as:

Seats = 56

When the bus is at half capacity, we have:

Seats = 28

As the price decreases by $5, the rider gains 2 more.

So, the revenue equation is:

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

Expand

y = 4368 - 140x + 312x - 10x²

Differentiate

y' = 0 - 140 + 312 - 20x

Evaluate the sum

y' = 172 - 20x

Equate to 0

172 - 20x =0

Add 20x to both sides

20x = 172

Divide both sides by 20

x = 8.6

Substitute x = 8.6 in y = (156 - 5x)(28 + 2x)

y = (156 - 5 * 8.6)(28 + 2 * 8.6)

Evaluate

y = 5107.6

Hence, the maximum revenue the bus company can earn is $5107.6

#SPJ1

Read more about revenue equations at:

https://brainly.com/question/19104371

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