Answer: Rmax = 50,000 dollars
Step-by-step explanation: from the question,
x= number of units sold
p(x) = price function = 200 - 0.2x
Revenue = price * quantity
Revenue = x ( 200 - 0.2x)
Revenue = 200x - 0.2x².
Let R = revenue, R = 200x - 0.2x²
To get the maximum revenue (Rmax), we need the maximum quantity (Xmax) that will produce that.
And to get maximum quantity, we equate the first derivative (dR/dx) of the revenue (R) with respect to quantity (x) to zero..
If R = 200x - 0.2x²
dR/dx = 200 - 0.4x = 0
200 - 0.4x = 0
200 = 0.4x
x = 200/ 0.4
x = 500
Hence Xmax = 500 units
Substitute Xmax into the revenue function to get maximum revenue,
R = 200x - 0.2x², but x = 500
Rmax = 200(500) - 0.2 (500)²
Rmax = 100,000 - 50,000
Rmax = 50,000 dollars
