SOLUTION: A fundraising company charges $200 plate for a local charity and sells 300 tickets. For every $10 increase they will lose 5 ticket sales. What would they charge to make a maximum p
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Question 1085633: A fundraising company charges $200 plate for a local charity and sells 300 tickets. For every $10 increase they will lose 5 ticket sales. What would they charge to make a maximum profit and what is the profit?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the number of $10
increases in the ticket price
Let = the profit
------------------------------
[ profit ] = [ tickets sold ] x [ income from selling 1 ticket ]
----------------------------
This is a parabola with a maximum. Use the formula for
the ( n, P ) of the vertex ( maximum in this case )
---------------------------------------------------
where
So, for a maximum profit, they would charge:
$400 / plate
-------------------------------
To find the profit, , plug the value for
back into the equation:
The maximum profit is $1600
-----------------------------
Feel free to get a 2nd opinion if needed
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