Question

Find two positive numbers whose product is 100 and whose sum is a minimum.

Answer 1

S=a+b
but a= 100/b
S=100/b + b

dS/db=0=-100/b^2 +1

solve for b, then go back and solve for a.

Answer 2

i hope i got it right. The two numbers are 10 and 10?

Answer 3

Exactly right. It's just the same as finding a rectangle of maximum area for a given perimeter. It's always a square.

Answer 4

thanks guys!