Maximum Revenue: An oil producing country can sell 1 million barrels of oil a day at a price of $25 per barrel. If each $1 increase in price will result in a decrease of 50000 barrels per day in sales, what price will maximize the country's revenue? How many barrels will it sell at that price.

Question

Maximum Revenue: An oil producing country can sell 1 million barrels of oil a day at a price of $25 per barrel.  If each $1 increase in price will result in a decrease of 50000 barrels per day in sales, what price will maximize the country's revenue?  How many barrels will it sell at that price.

experimentx · Answer

let, x be the price of the barrel and y be the no of barrels sold
f(x,y) = xy
given that,
(x-1) = ... lol .. looks like i need answer keys afterall

experimentx · Answer

hmm ,, some kind of linear relationship i guess

precal · Answer

ok The country's revenue will be maximized if they decrease the price by selling each barrel of oil for $22.50 (from x=-2.5 price increases)

experimentx · Answer

y - 1000000 = -50000(x-25)

experimentx · Answer

y = 1000000 - 50000(x-25)
f(x,y) = x(1000000 - 50000(x-25)) = parabola opening down !!!

experimentx · Answer

I hate big numbers :D

precal · Answer

i agree

experimentx · Answer

Hmm ... looks like i got this http://www.wolframalpha.com/input/?i=maximize+x%281000000+-+50000%28x-25%29%29

experimentx · Answer

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