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Find 2 positive numbers whose product is 10,000 and whose sum is a minimum

x * y = 10000

x + y = S

y = 10000/x

x + 10000/x = S

x + (10000)(x ) = S

-1

derive and find where Sā€™ = 0 to find minimum

Sā€™ = 1 - (10000)(x )

-2

0 = 1 - (10000)(x )

-2

x = 100

y = 100