Answer to Question #259063 in Analytic Geometry for Ein

Question

The sum of two positive numbers is 50. what are the numbers if their product is to be the largest possible.

CHOICES:

25 and 25

20 and 30

24 and 26

28 and 22

Answer 1

Let $x=$ the first number. Then the second nmber will be $50-x.$

$0<x<50$

Their product will be

$$f(x)=x(50-x)=-x^2+50x$$

The quadratic function $f(x)$ has the absolute maximum at $x=-\dfrac{50}{2(-1)}=25.$

$50-25=25.$

25 and 25