Word Problem - finding mass transit fares

[LM1]

Hello,

Can anyone give me some advice on where to start with this problem. I was able to get the answer in excel but I would like to know how to do it on paper. It is from my college algebra class and from the chapter on functions. Below is the problem.

The municipal transit authority serves 150,000 commuters daily when the fare is $1.80. Market research has determined that every penny decrease in the fare will result in 1,000 new riders. What fare will maximize revenue?

Please help!!!

 

[Mrspi]

Hello,

Can anyone give me some advice on where to start with this problem. I was able to get the answer in excel but I would like to know how to do it on paper. It is from my college algebra class and from the chapter on functions. Below is the problem.

The municipal transit authority serves 150,000 commuters daily when the fare is $1.80. Market research has determined that every penny decrease in the fare will result in 1,000 new riders. What fare will maximize revenue?

Please help!!!

Let x = number of $0.01 decreases in the fare

The new fare will be $1.80 - 0.01x

Since each decrease of $0.01 in the fare results in an INCREASE of 1000 riders, after x such decreases, the number of riders will increase by 1000x.

New number of riders will be 150000 + 1000x

Revenue = number of riders * fare per rider

Revenue = (150000 + 1000x)(1.80 - 0.01x)

Now...expand the right side by multiplying the binomials together. You'll get a quadratic function whose graph is a parabola which opens DOWNWARD. The maximum revenue occurs at the vertex of the parabola.

Your turn to do some work!