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 pe
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Question 1155580: The weekly profit(in dollars) of a company making and selling x virtual pets each week is given by . What is the maximum profit, and how many virtual pets should be made and sold each week to maximize profit?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
-x^2 + 980x - 3000 is quadratic equation, the max value is on the axis of symmetry.
Use the formula x = -b/(2a), where a=-1; b=980
x =
x = +490 items sold for max profit
:
Find the actual profit at his value
P(x) = -490^2 + 980(490) - 3000
P(x) = -240100 + 480200 - 3000
P(x) = $237,100 profit
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The formula for the x-value of the vertex
( maximum in this case ) is:
Plug this result back into equation:
-------------------------------
There maximum ;profit is $237,000
and the number of virtual pets sold
is 490
--------------------
check:
Here's the plot:
Looks about right
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