Solve the problem.The price p dollars and the quantity x sold of a certain product obey the demand equation
x= -15p + 450; 0 < p < 30
a) express the revenue r as a function
b) what quantity x maximizes the revenue?
c) What price should the company charge to maximize revenue?
x= -15p + 450; 0 < p < 30
a) express the revenue r as a function
b) what quantity x maximizes the revenue?
c) What price should the company charge to maximize revenue?
-
X= -15p +450
(x-450)/(-15) = p
p= (-1/15)x + 30...this is the demand function for price in terms of x
A) Revenue = R(x)= px = (-1/15)x^2 + 30x
B) this is a parabola that opens down. The max is at the vertex. You can find it by graphing, by calculus (R'= 0) or by x= -b/(2a)
X= -30/(-2/15)=225
C) p= (-1/15)(225)+30= 15
Hoping this helps!
(x-450)/(-15) = p
p= (-1/15)x + 30...this is the demand function for price in terms of x
A) Revenue = R(x)= px = (-1/15)x^2 + 30x
B) this is a parabola that opens down. The max is at the vertex. You can find it by graphing, by calculus (R'= 0) or by x= -b/(2a)
X= -30/(-2/15)=225
C) p= (-1/15)(225)+30= 15
Hoping this helps!