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
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.
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.