quadratic equation max and min problem

Question

A transit company charges $1.25$ dollars per ride and currently averages $10,000$ riders per day. The company needs to increase revenue but found that for each $0.10$ dollars increase in fare the company would lose $500 $ riders. What should the company charge to maximize revenues?

Please form an equation for me to solve this. i've tried multiple times and am not getting the right answer. the answer should be $0.75$ dollars raise to a new fare of $2.00$ dollars

Answer 1

Hint: Revenue of the day $=$ Charge per ride $\times$ Number of rides per day.

Charge per ride $ = 1.25 + 0.1x$

Number of rides per day $ = 10,000 - 500x$,

$x = $ the number of times the fees is increased.

Thus $R(x) = (1.25+0.1x)(10,000-500x)$.

Can you use the vertex method again to find the max for $R$?

Answer 2

Hints:

• Can you express the number of riders as a function of the fare?

  • The question says this is linear, and gives you a point and the gradient.

• Can you express the revenue as a function of the fare?

  • The revenue is the fare multiplied by the number of riders.

• Can you find the fare which maximises revenues?

  • For example you might look at the derivative of the function for the revenue with respect to the fare.