Question-1: Consider the following function (50 marks) f (x, y, z) = (x2 + 2v3)e-(x2+12) (i) Find all the stationary points. (ii) Determine their type of stationary points. (iii) Is this function concave over its domain? Prove your answer. Now suppose we have the following constrained problem: max(x +2x3)e-(x2+y?) subject to x+ ys0 (iv) Find the solution for the constrained problem. (v) Check whether the solutions are in fact maximum. (vi How much does the value of the maximum of the function changes if 2 changes to 2.1 in the objective function