$5$pts$.5$ pts per part. Find candidate solutions to the following problem using the KKT

conditions and the listed steps:

min x$2$

$1+$ x$2$

$2(1)$

subject to: x$2>=$x$1+1(2)$

x$2>=$ x$1+1(3)$

$$ a$.$ Re$-$format the problem in the correct form for the KKT conditions

$$ b$.$ Write the Lagrangian for this problem

$1$

$$ c$.$ Write the equations provided by the KKT conditions

$$ d$.$ Write the $4$ cases created by the complementarity condition for this problem

$$ e$.$ Solve for the candidate solution