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)
P = {{{-1/5}}}x + 140
:
A) how much should be charged for a barrel of oil on hand
One barrel of oil on hand ( in millions)
P = {{{-1/5}}}(1) + 140
P = -.20 + 140
P = $139.80
:
B) what quantity x will maximize revenue?
Rev = quantity * price
R = x({{{-1/5}}}x + 140)
R = {{{-1/5}}}x^2 + 140x
This is a quadratic equation; max occurs at he axis of Symmetry, x = -b/(2a)
therefore
x = {{{(-140)/(-2/5)}}}
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 = {{{-1/5}}}(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