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 $1.50. How many boxes must be sold each mont
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$ x(5-0.05x). The wholesale cost of each box of candy is $1.50. How many boxes must be sold each mont
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Question 39412: 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 josmiceli(19441) (Show Source):
You can put this solution on YOUR website! This is a workout for my calculator!
It's asking for Profit, so I rewrite
Revenue = Cost + Profit
Profit = Revenue - Cost (P = R - C)
The cost of 1 box is 1.50, so the cost of x boxes is 1.5x
If I find the roots, the maximum will be midway between
the 2 roots. Set P = 0 to find roots.
multiply both sides by -1
The roots are 0,70. The midpoint is (0 + 70)/2 = 35
I want to test the equation for P to see if 35 is really
a maximum. I will find P(34), P(35), and P(36).
P(34) and P(36) should both be slightly less than P(35)
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So, 35 boxes must be sold each month to maximize Profit,
which is $61.25
