P=-1/5x+148

Question

he 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 2 million barrels on hand?
b) What quantity x will maximize revenue?
c) What price should be charged in order to maximize revenue?
p=-1/5x+148

Answer 1

P(x) = -(1/5)x + 148

 

where x = millions of barrels of oil.

 

a) How much should be charged for a barrel of oil if there are 2 million barrels on hand?

 

x = 2 (remember, x is millions of barrels)

P(2) = -(1/5)(2) + 148 = _______?

 

b) What quantity x will maximize revenue?

Revenue is (price per barrel)*(number of barrels sold)

 

R = p*x = -(1/5)x² + 148x

 

This is an inverted parabola with its vertex at x = -b/2a = -(148)/2(-1/5) = 370 million barrels. The vertex is the highest (maximum) point on the revenue curve, so 370 million barrels will maximize revenue.

 

c) What price should be charged in order to maximize revenue?

 

P(370) = (-1/5)(370) + 148 = ________