The two functions are graphed and attached
The price at the two breakeven points are p = 12.66 and p = 38.42
The revenue and expense amounts for each break even points are 84303 and 72711
The maximum revenue is $328300 at a price of $24.32
Graphing the two functions and find the price at the two breakeven points.
From the question, we have the following parameters that can be used in our computation:
E = -450p + 90000
R = -185p² + 9000p
The price at the two breakeven points is the point where the functions intersect
The graph is added as an attachment and the price at the two breakeven points are p = 12.66 and p = 38.42
How to determine the revenue and expense amounts for each break even points
We have
p = 12.66 and p = 38.42
For the expense function, we have
E = -450 * 12.66 + 90000 = 84303
E = -450 * 38.42 + 90000 = 72711
For the revenue function, we have
R = -185 * 12.66² + 9000 * 12.66 = 84303
R = -185 * 38.42² + 9000 * 38.42 = 72711
What price will yield the maximum revenue?
Here, we have
R = -185p² + 9000p
Differentiate
R' = -370p + 9000
Set to 0
So, we have
-370p + 9000 = 0
370p = 9000
Divide
p = 24.32
This means that the maximum revenue is
Max R = 185 * 24.32² + 9000 * 24.32
Max R = 328300
Hence, the maximum revenue is $328300
