Set up the following problem in its Lagrange multiplier form. Note that the non-negativity condition on x2 must be handled explicitly as an additional constraint. show the Lagrangian function and derive the related necessary conditions. Verify that the following solution satisfies the necessary conditions: x1=5, x2=5. Relaxing which constraint would yield the greatest improvement in the objective function? Optimize Z=4x1x2+x1 Subject to: x1<5 x1+x2=10 with x1 unrestricted, x2>0.