Question #259063

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

1
Expert's answer
2021-11-03T17:59:12-0400

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

0<x<500<x<50

Their product will be


f(x)=x(50x)=x2+50xf(x)=x(50-x)=-x^2+50x

The quadratic function f(x)f(x) has the absolute maximum at x=502(1)=25.x=-\dfrac{50}{2(-1)}=25.

5025=25.50-25=25.


25 and 25



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