Question

The dollar price for a barrel of oil sold at a certain oil refinery tends to follow the demand equation below, where x is the number of barrels of oil on hand (in millions). ​

(Each question is individual. NOT MULTIPLE CHOICE.)
a) How much should be charged for a barrel of oil if there are 9 million barrels on ​ hand?
​b) What quantity x will maximize​ revenue? ​
c) What price should be charged in order to maximize​ revenue?

p = - 1/10 x + 74

Answer 1

p= -1/10x+74
we can write this as
p = -.10x + 74
a) How much should be charged for a barrel of oil if there are 9 million barrels on ​ hand?
p = -.10(9) + 74=73.1 a barrel
​b) What quantity x will maximize​ revenue?
r(x) = x(-.10x + 74)
r(x) = -.10x^2 + 74x
Find the axis of symmetry of this equation x = -b/(2a)
x = -74/(2*(-0.10))=370x = 370 million barrels

c) What price should be charged in order to maximize​ revenue?
p = -.10(370) + 74
p = -37 + 74
p = $37 a barrel