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

(a)$173.50

(b)350 Million

(c)$87.50 per barrel

Step-by-step 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,

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

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is