SOLUTION: the dollare 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) h

Algebra ->  Functions -> SOLUTION: the dollare 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) h      Log On


   

Question 934641: the dollare 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 on hand
B) what quantity x will maximize revenue? what is the maximum revenue
C) what prcies should be charged in oreder to maximize revenue
P=-1/5x+140
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the dollare 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)
P = -1%2F5x + 140
:
A) how much should be charged for a barrel of oil on hand
One barrel of oil on hand ( in millions)
P = -1%2F5(1) + 140
P = -.20 + 140
P = $139.80
:
B) what quantity x will maximize revenue?
Rev = quantity * price
R = x(-1%2F5x + 140)
R = -1%2F5x^2 + 140x
This is a quadratic equation; max occurs at he axis of Symmetry, x = -b/(2a)
therefore
x = %28-140%29%2F%28-2%2F5%29
x = +350 million barrels of oil on hand for max revenue
"what is the maximum revenue?'
Find the price when 350 m barrels are on hand
P = -1%2F5(350) + 140
P = -70 + 140
P = $70 a barrel for max rev
Max revenue: 70 * 350 million = $24,500 million
:
C) what price should be charged in order to maximize revenue
$70 a barrel