I heard that the answer will be like this, but I would like to know the solution to lead me to the answer.

I can answer the Kuhn-Tucker Condition, but then I don't know how to get the answer. I would like to know.

(SM) 4. Consider the problem max x+ay s.t. x2+y21 and x+y0, where a is a constant. (a) Sketch the admissible set and write down the necessary conditions. (b) Find the solution for all values of the constant a. SM) 5. Solve the following problem, assuming it has a solution: 4. (a) The admissible set and one of the level curves for x+ay are shown in Fig. A14.9.4. The requested necessary conditions, with C=x+ay(x2+y21)+(x+y), are: (i) Lx=12x+=0; (ii) Ly=a2y+=0 (iii) 0, with =0 if x2+y20; (v) x2+y21: (vi) x+y0. (b) The solution is (x,y)=(212,212) in case a1, but (x,y)=(1/1+a2,a/1+a2) in case a>1