Question

A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price.

Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements.

-100x^2 + 1,500x + 10,000 >/= 12,000
100x^2 - 1,500x - 10,000 >/= 12,000
The price of a one-way ticket that will maximize revenue is $12.50.
The price of a one-way ticket that will maximize revenue is $7.50.
The maximum profit the company can make is $4,125.00.
100x^2 + 1,500x - 10,000 = 12,000
The maximum profit the company can make is $15,625.00.

Answer 1

(2000 - 100x)(5 + x)》12000

10000 - 500x + 2000x - 100x²》12000

-100x² + 1500x + 10000》12000

x for max profit:

-200x + 1500 = 0

x = 7.5

Price = 5 + 7.5 = 12.5

Max profit:

(2000 - 100(7.5))(5 + 7.5)

= 1250 × 12.5

= $15625