The dollar price for a barrel of oil sold at a certain oil r

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). How much should be charged for a barrel of oil if there are 6 million barrels on hand? What quantity x will maximize revenue? What price should be charged in order to maximize revenue? P = - 1/4 x + 180 What should be charged for the units in stock? (Round to the nearest cent as needed.) What quantity will maximize the revenue? million units What price should be charged for the maximum revenue? (Round to the nearest cent as needed.)

Solution

p = -x/4 + 180

a) x= 6 million barrel

plug x= 6 in the equation :

p = -6/4 +180 = $178.5

b) Revenue ; R(x) = x*p = -x^2/4 +180x

For quadratic ax^2 +bx +c function maximum occurs at vertex given by x= -b/2a

x= -(180)/(-2*1/4) = 360 million barrel units

c) Price charged for maximu revenue:

p(360) = -360/4 +180 = $ 90