SOLUTION: the monthly revenue achieved by selling x boxes of candy is calculated to be $ x(5-0.05x). the wholesale cost of each box of candy is $1.50. How many boxes must be sold each month

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Question 40035: the monthly revenue achieved by selling x boxes of candy is calculated to be $ x(5-0.05x). the wholesale cost of each box of candy is $1.50. How many boxes must be sold each month to maximize profit?
what is the maximum profit?
(Revenue=Cost +Profit)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
1. The monthly revenue achieved by selling x boxes of candy is caluculated
> to be $x(5-0.05x). The wholesale cost of each box of candy is $1.50.
c.p of x boxes = 1.5x
profit =p= x(5-0.5x)-1.5x=5x-0.5x^2-1.5x
=3.5x-0.5x^2=-0.5{x^2-2x*3.5+3.5^2}+0.5*3.5^2
0.5*3.5^2-0.5(x-3.5)^2...hence to get maximum profit theoretically
x=3.5..since this is not possible as x cannot be fraction x=4 or 3 is
the answer
at =4 ..we get
p=0.5*3.5^2-0.5*0.5^2= 6
How many boxes must be sold each month to maximize profit? What is the maximim
> profit?
>