Question 20737: The executives of the world famous " A slice of Pi" mathematics journal have determined that the cost of printing m magazines is one-third of the square of the number of magazines produced. Furthermore, they have dtermined that the revenue generated from seliing m magazines is 5 dollars more that twice the number of magazines sold. Assuming every copy of "A slice of Pi" magazine printed is always sold, how many magazines must they print in order to maximize their profit, AND what is the maximum profit? (hint: profit= Revenue- cost) I am completly lost excpet 1/3m2 Please HELP!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let number of magazines produced be "m".
Then Cost = (1/3)m^2
And Revenue = 2m+5 dollars
EQUATION:
Profit = Revenue - Cost
Profit = 1/3 m^2-2m-5
This is a quadratic with a=1/3, b=-2, c=-5
The max is at m=-b/2a= 2 divided by 2/3 = 3
Wow! Greatest profit when they produce
3 magazines. Seems unreasonable.
Cheers,
Stan H.
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