SOLUTION: (40 points) A Middle Eastern oil-producing country estimates that the demand for oil (in millions of barrels per day) is D(p) = 9.5 e^(-0.04p), where p is the price of a barrel of

Question 1125309: (40 points) A Middle Eastern oil-producing country estimates that the demand for oil (in millions of barrels per day) is D(p) = 9.5 e^(-0.04p), where p is the price of a barrel of oil. To raise its revenues, should it raise or lower its price from its current level of $120 per barrel?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the equation of D = 9.5 * e^(-.04 * P) tells the demand based on the price per barrel.

revenue is equal to demand * price.

demand is presumably in millions of barrels of oil.

the price is presumably price per barrel.

since revenue = demand * price, you can determine the reveue by using the following equation.

y = 9.5 * e^(-.04 * x) * x.

y is the revenue, in millions of dollars.
9.5 * e^(-.04 * x) is the demand, in millions of barrels of oil.
x is the price per barrel.

note:

millions of barrels of oil is assumed.
it could be any unit multiple, such as thousands of barrels of oil, or billions of barrels of oil.
i assumed millions, because that seems to be a common unit multiple used when talking about daily production of barrels of oil world wide.
it really doesn't matter, since the revenue curve is unit independent, i.e. the same conclusions can be formed regardless of the units of measure used.

what i did was graph the equation of y = 9.5 * e^(-.04*x) * x.

the graph is shown below:

$$$

the graph shows that the revenue will get greater as the price of oil goes down until the price becomes 25 dollars a barrel, when the revenue is maximized at 87.371 million dollars (assuming millions of barrels is the unit of measure).

any price below that will lead to a decrease in revenue from that peak.

any price above that will leas to a decrease in revenue from that peak.

based on this graph, the solution is that reducing the price down from 120 a barrel will result in an increase in revenue as long as the price doesn't go below 25 dollars a barrel.

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