Consider two nonnegative numbers x and y such that x + y = 12. Find the values of x and y that optimize the following quantity. (If an answer does not exist, enter DNE.)

Question

The following quantity = y-1/x

Maximize the quantity: {x, y} = { ,  }

Minimize the quantity: {x, y} = {  , }

Answer 1

Answer would be DNE, for both, except the problem requires non negative numbers

so

the answer is (12,0) for minimum y-1/x

and DNE for maximum,

(0,12) would the maximum but y-1/x = 12-1/0 is undefined