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). ​a) How much should be charged for a barrel of oil if there are 6 million barrels on ​ hand? ​b) What quantity x will maximize​ revenue? ​c) What price should be charged in order to maximize​ revenue? p= -1/4x+175

Answer 1

(a)$173.50

(b)350 Million

(c)$87.50 per barrel

Explanation:

P=-1/4x+175

P=-0.25x+175

(a)If there are 6 million barrels of oil on hand,

x=6

P=-0.25(6)+175

=-1.5+175

Price=$173.5

(b)If the Price Per barrel

P=-0.25x+175

To determine the quantity x,that will maximize revenue, we determine at which point the revenue generated, xP will be maximum.

xP=x(-0.25x+175)

Revenue, R(x)=-0.25x²+175x

We determine the axis of symmetry of the function,

Axis of Symmetry, [TeX]x=-\frac{b}{2a}[/TeX]

[TeX]x=350[/TeX]

350 Million barrels must be sold to maximize revenue.

(c)In order to maximize revenue(at 350 million barrels)

The Price,P=-0.25(350)+175

=$87.5 per barrel