Question

A shuttle service charges each customer $10.00 for a ride from the airport to the hotel. It costs $45.00 each time the shuttle driver must fill up the gas tank. The shuttle company wants to make a profit of at least $6,000.00. (1) Designate variables for any unknown values. (2) Write an appropriate constraint to represent this scenario.

Answer 1

1. Variables:

x is the profit

y is the number of customers

z is the number of times the shuttle driver must fill up the tank

2. 10y-45z ≥ 6,000

Explanation:

The variables for unknown values are:

x is the profit

y is the number of customers

z is the number of times the shuttle driver must fill up the tank

According to the statement, the company wants to make profits of at least $6,000 and the profits are equal to the total sales minus the costs.

Sales= Price per customer*number of customers= 10x

Costs= Price per each time the tank must be filled*number of times the shuttle driver must fill up the tank= 45y

z=10y-45z where z
`\geq` 6,000

This means that 10y-45z
`\geq` 6,000.