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 refiner) 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 8 mil ion barrets on hand? What quantity x will maximize revenue? What price should be charged in order to maximize revenue? p = 1/10 x 70 What should be charged for the units in stock? What quantity will maximize the revenue? What price should be charged for the maximum revenue?

Solution

Given : P = (-1/10)x + 70

Part A : There are 8 million barrels on hand. So, we will plug x=8 into above equation. So, we get :

P = (-1/10) (8) + 70 = $ 69.2 (Answer)

Part B : Revenue = Price * Quantity

= [(-1/10)x + 70] * x

= -0.1 x² + 70x

Maximize means we will find the vertex. The vertex is given by x=-b/2a.

So, x = -70/2(-0.1) = 350 (Answer for Part B)

Part C : We will plug x=350 into P = (-1/10)x + 70

So, P = (-1/10)(350) + 70

= 35 (Answer for Part C)