The following objective function has been given

Subjected to constraints

minJ$=x_1^2-10x_2^2+5x_3^2+13x_1-23x_2$

Subjected to const

$20x_2-3x_{3}25$

$x_1-11x_{3}11$

$3x_1+4x_{2}8$

Write the Karush$-$Kuhn$-$Tucker conditions for the above system. Solve the above$-$given equations using the Karush$-$Kuhn$-$Tucker technique. Provide the value for each variable $x_1,x_2,x_3$ and slackness variables after the solution.

$[5]$