The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x=-5p+200. What price p maximizes revenue?
p=$
To maximize revenue, we need to find the price that maximizes the product of price and quantity (revenue = price * quantity).
Substitute x=-5p+200 into the revenue equation:
R(p) = p(-5p+200)
R(p) = -5p^2 + 200p
To find the price that maximizes revenue, we need to find the vertex of the parabola represented by the equation R(p) = -5p^2 + 200p.
The x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a).
In this case, a = -5 and b = 200.
p = -200/(2*-5)
p = -200/-10
p = 20
Therefore, the price that maximizes revenue is $20.