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.
Answers
x² - 15x + 20 < 0 inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000
Step-by-step explanation:
A carpool service has 2,000 daily riders.
A one-way ticket costs $5.00
Revenue = 2000 * 5 = 10000 $
for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation
Let say Fare increased x $ then 100x passengers will be reduced
=> Revenue = (2000 - 100x) (5 + x)
(2000 - 100x) (5 + x) > 12000
=> 10000 + 1500x - 100x² > 12000
=> 1500x - 100x² > 2000
=> 15x - x² > 20
=> x² - 15x + 20 < 0
Revenue = 10000 + 1500x - 100x²
dR/dx = 1500 - 200x
=> x = 7.5
d²R/dx² = -200
x = 7.5 give maximum revenue
= 1250 * 12.5 = 15,625
x = 7 1300 * 12 = 15600
x = 8 12000 * 13 = 15600
Learn more about inequalities :
hens should be bought in order to have a maximum profit per week.
https://brainly.in/question/9077084
https://brainly.in/question/11507005