A transit company carries about 80,000 riders per day for a fare of $1.25. To obtain more revenue, the management plans to increase the fare........
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It estimates that for every 5 cent increase in fare, it will lose 1000 riders. What fare would result in the greatest revenue and what would the maximum revenue be?
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What you need to do here is to set up a table. Your table should have three columns -- the fare, the number of riders per day, and the total revenue. Revenue will, of course, be the fare multiplied by the number of riders.
Then you just start plugging in numbers -- it's easy to do this using Excel. When you do this, you find that a price of either $2.60 or $2.65 will get you the same amount of revenue. In each case, your revenue will be $137,800. This is the highest revenue level.
If you want to solve this mathematically, you will need to derive the equation for a parabola where the x axis is the revenue and the y axis is the fare. Then you will need to use that equation to find the vertex of the parabola.
Please see the following link for how to find the equation of a parabola given three points on that parabola.
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