Question

Max points need asap algebra 2

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

-100x² + 1500x + 10000》12000

Price = $12.5

Max profit = $15625

Step-by-step explanation

(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

Answer 2

-100x^2 + 1,500x + 10,000 >= 12,000

The revenue will maximize at 12.50

The maximum profit the company can make is $15,625.00.

Explanation:

revenue =( ticket) * price

x is the price increase

for each 1 increase we lose 100 passengers, so for each x we increase, we lose 100x passengers

(2000-100x) (5+x)

-100x^2+1500x+10000

This must be greater than 12000

-100x^2 + 1,500x + 10,000 >= 12,000

Subtract 12000 from each side

-100x^2 + 1,500x + 10,000 -120000>= 0

-100x^2 + 1,500x -2,000 >= 0

Taking the derivative

-200x +1500 and setting it equal to zero

-200x +1500=0

-200x=-1500

x = 1500/200

x = 15/2

To find the max value of the ticket take x and add 5 to find the ticket price

The max is at 12.5

The revenue will maximize at 12.50

To find the maximum revenue, put 7.50 into the equation (x=7.5 which is the price increase)

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

(2000-750) (12.5)

1250*12.5

15625