SOLUTION: The weekly profit(in dollars) of a company making and selling x virtual pets each week is given by P(x)= -x^2+980x-3000. What is the maximum profit, and how many virtual pets shoul

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Question 1155517: The weekly profit(in dollars) of a company making and selling x virtual pets each week is given by P(x)= -x^2+980x-3000. What is the maximum profit, and how many virtual pets should be made and sold each week to maximize profit?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for profit is P%28x%29=+-x%5E2%2B980x-3000
At the value of x where this function (profit) is maximum, the first derivative of the formula will be 0.
i.e. -2x+%2B+980+=+0
or x+=+980+%2F+2+=+490
490 virtual pets will yield the maximum profit.
The maximum profit can be found by substituting x = 490 in the formula
Max profit = P(490) = -%28490%5E2%29+%2B+980x490+-+3000+=+237100
Ans: 490 pets, profit $237100