Question 504161: solving max/min problems: the sum of two positive number is 56.Find the two numbers,if their product ia amaximum. Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! If the two numbers are a and b, then a+b = 56 which can be written as a = 56-b.
Now a*b must be a maximum (call it y)so we can write a*b as: Simplify. This is a quadratic equation and the graph will be a parabola opening downward.
So all you need to do to find the maximum is find the value of b at the point of the parabola's vertex which is given by:
So the two numbers are: a = 28 and b = 28.
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