The price p and x, the quantity of a certain product sold, obey the demand equation
p= -1/10x + 100, 0 < x < 1000.
a) express the revenue R as a function of x
b) what is the revenue if 450 units are sold?
c) what quantity x maximizes revenue? What is the maximum revenue?
d) what price should the company charge to maximize revenue?
Very confused...
p= -1/10x + 100, 0 < x < 1000.
a) express the revenue R as a function of x
b) what is the revenue if 450 units are sold?
c) what quantity x maximizes revenue? What is the maximum revenue?
d) what price should the company charge to maximize revenue?
Very confused...
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a) R(x) = px = (-1/10x + 100) x) = 100 x - 1/10 x^2
b) R(450) = 100. 450 - 1/10 450^2 = 45000 - 20250 = 24750
c) max: R'(x) = 0
100- 1/5 x = 0
100 = 1/5 x
x = 500
R(500) = 100. 500 - 1/10 500^2 = 50000 - 25000 - 25000
d) p(500) = -1/10 500 + 100 = -50 + 100 = 50
b) R(450) = 100. 450 - 1/10 450^2 = 45000 - 20250 = 24750
c) max: R'(x) = 0
100- 1/5 x = 0
100 = 1/5 x
x = 500
R(500) = 100. 500 - 1/10 500^2 = 50000 - 25000 - 25000
d) p(500) = -1/10 500 + 100 = -50 + 100 = 50