Problem $2$ Solve the nonlinear optimization problem

minf$(x_1,x_2)=(x_1{)}^2-x_1{x}_2+(x_2{)}^2-2x_2$

$s.t.g(x_1,x_2)=x_1+x_2-10$

$($a$)$ Apply the optimality conditions;

$($b$)$ Verify your solution i Excel.