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

v v cj van config k tbs eng r.c r.c fcb fb gb frfr

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°