A bus company carries about 20,000 riders per day at a fair of $.90. If the fair is decreased by five cents, the number of riders will increase by 2000. What ticket price will generate the most revenue

Answer 1

To find the ticket price that generates the most revenue, we need to use the formula:

Revenue = Price x Quantity

Let's first calculate the current revenue:

Price = $0.90
Quantity = 20,000

Revenue = $0.90 x 20,000 = $18,000

Now let's calculate the revenue when the price is decreased by five cents:

Price = $0.85
Quantity = 20,000 + 2,000 = 22,000

Revenue = $0.85 x 22,000 = $18,700

Now let's repeat this process for different price levels to see which one generates the most revenue:

Price | Quantity | Revenue
------|----------|--------
$0.80 | 24,000 | $19,200
$0.75 | 26,000 | $19,500
$0.70 | 28,000 | $19,600
$0.65 | 30,000 | $19,500

Based on these calculations, it appears that a ticket price of $0.70 generates the most revenue, with a total of $19,600.

Answer 2

all that work!
Suppose there are x 5¢ decreases. Then the revenue will be
(0.90-0.05x)(20000+2000x) = -100x^2 - 800x + 18000
The maximum revenue will be at the vertex of this parabola, which occurs at (4,19600). Same as shown above.