Quadratic Functions

Question

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. It estimates that for every 5 cent increase in fare, it will lose 1000 riders. Determine the maximum revenue.

Answer 1

Complex problem, price per ride = 1.25 + 0.05x ; number of riders = 80,000 - 1000x

Toal income = price per ride times number of riders so (1.25 + 0.05x)(80,000 -1000x)

multiply to get quadratic, put in standard form solve for x coordinate of vertex -b/2a to get

the number of times you should raise rate by 5 cents to yield maximum profit.

I hope this helps