A tolled facility currently carries 12000 vehicle per day, with the current toll

Question

A tolled facility currently carries 12000 vehicle per day, with the current toll being 2$ per vehicle. studies have shown that for each increase in toll of 75 cents per vehicle, the traffic volume would decrease by 1200 vehicle per day. It is desired to increase the toll to a point where revenue will be maxmized.

a) let x represent the toll increase in cents. Write the expression travel demand on the bridge,related to toll increase and current volume

b) Determine what the toll charge should be to maximize revenues

c) Determine what the traffic volume per day whould be when the toll charge is set to that required to maximize revenues

d) Determine the increase in total revenue with the new toll charge described in part b.

Explanation / Answer

a.)If 75 cents reduces traffic volume by 1200 vehicles, 1 cent reduces traffic by 16 .(1200/75 = 16)
So the traffic on the bridge will be:

T = 12,000 - 16x

The current toll of $2 does not enter into the equation.

b.) Revenue = Traffic volume*toll charge = (12000 - 16x)(200+x)

So R = 2400000 + 12000x - 3200x - 16x^2

dR/dx = 0

12000 - 3200 - 32x =0

So x = 275

So Toll charge = 200 + 275 = 475 cents = $4.75

c.) Traffic Volume = 12000 - 16(275) = 7600

d.) Old Revenue = 12000*2 = $24,000

New Revenue = 7600*4.75 = $36,100

So Increase in Total Revenue = $36,100 - $24,000 = $12,100

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