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

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