SOLUTION: The price p(in dollars) and the quantity x sold of a certain product obey the demand equation p=-1/5x+20 , 0<=p<=20 A.express the revenue R as a function of x B. What is the

Algebra ->  Trigonometry-basics -> SOLUTION: The price p(in dollars) and the quantity x sold of a certain product obey the demand equation p=-1/5x+20 , 0<=p<=20 A.express the revenue R as a function of x B. What is the      Log On


   

Question 1204672: The price p(in dollars) and the quantity x sold of a certain product obey the demand equation p=-1/5x+20 , 0<=p<=20
A.express the revenue R as a function of x
B. What is the revenue if 15 units are sold?
C.what quantity x maximizes revenue?
D. What price should the company charge to maximize revenue?
Answer by mananth(16946) About Me  (Show Source):
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The price p(in dollars) and the quantity x sold of a certain product obey the demand equation p=-1/5x+20 , 0<=p<=20
A.express the revenue R as a function of x
R= p*x
R= ((-1/5)x+20)*x
R = (-1/5)x^2+20x
B. What is the revenue if 15 units are sold?
R = (-1/5)x^2+20x
R= (-1/5)*15^2+20*15
R=$255
C.what quantity x maximizes revenue?
R = (-1/5)x^2+20x
dR/dx= -(2/5)*x+20
To maximise set the derivative to 0
-(2/5)*x+20=0
2/5*x=20
x=100/2
x= 50
D. What price should the company charge to maximize revenue?
Maximum units 50
P= -1/5*50+20
-10+20
=10
The company should charge $10 to maximize revenue when selling 50 units.