Question

find two positive numbers A and B with A less than or equal to B whose sum is 52 and whose product is mazimized

Answer 1

26 and 26

Explanation:

Let's call the two numbers x and 52-x.

Their product is
`p(x) = x(52-x)=52x-x^2`. Now, if you know calculus, you take it's derivative, see where it goes to 0, and determine what kind of critical point is that. Or - especially if you don't know what a derivative is - you stare at it long enough, and realize that that's the equation of a parabola. pointing downward. It means it has a maximum at its vertex, and the vertex has its first coordinate in the point
`x_v= -(b)/(2a) = -(52)/(2)(-1)) = 26` The two numbers are, then 26 and 52-26=26.