SOLUTION: 4800 vehicles use the tollway for free. After the first month it is estimated that for each dollar increase in the toll, 800 fewer vehicles will use the tollway. At what price do y

Question 894291: 4800 vehicles use the tollway for free. After the first month it is estimated that for each dollar increase in the toll, 800 fewer vehicles will use the tollway. At what price do you think the company should set the tolls in orders to make the most money? Why?
Found 3 solutions by josgarithmetic, MathTherapy, richwmiller:
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!
x for how many dollars toll price
q for how many vehicles use tollway

VEHICLES________PRICE
4800____________0
4000____________1
3200____________2
2400____________3

Let r = revenue.
----revenue is number of vehicles multiplied by the price for each vehicle.

Substitute for q in r.

This is a parabola with vertex as a maximum.

The zeros of r occur at and for , and the maximum for r occurs in the middle of these roots.

The nonzero root:

The two roots for r are at 0 and 6.
The midpoint of those is .
The maximum revenue would be predicted at 2 dollar per vehicle.
You can evaluate the estimated revenue if you want.
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

4800 vehicles use the tollway for free. After the first month it is estimated that for each dollar increase in the toll, 800 fewer vehicles will use the tollway. At what price do you think the company should set the tolls in orders to make the most money? Why?

Maximum revenue will occur when price is set at: $
You can do the check!!
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Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
fixing josgarthmetic's answer
The two roots for r are at 0 and 6.
The midpoint of those is (0+6)/2=3
The maximum revenue would be predicted at 3 dollar per vehicle.

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