I am struggling with the following question:
Solve the following programing problem:
max $f(x_1,x_2)$= $ \sqrt{(x_1 + 1) (x_2+1)} $ subject to $x_2-(x_1-1)^2 \leq 0 $; $x_1+x_2 \leq 7 $; $x_1, x_2 \geq 0$ Using the Karush-Kuhn-Tucker condition, I can proof that the cases: - $x_1 = 0 $ $x_2=0 $ - $x_1 = 0 $ $x_2 > 0$ - $x_1 > 0 $ $x_2 > 0$ Are not valid solutions for the problem. But I don't get a hang on proofing the last case ($x_1 > 0; x_2 > 0$) and actually finding a solution algebraically for the problem. Thank you!