W (e) (Grid Search, Original Problem.) Let fr,y) = 3.0 * + 2y 4* + 2xy and g(2,y) = 1 +y-1 denote the original function we seek to maximize and let g(x,y) = x + y-1 denote the original constraint. Conduct a grid search using the following set of start points, {(ty) {-1, -0.99,-0.98,...,0.99, 1}x+y (0.991, 1.009]}. What is the optimal (2*,y*) from this search and how does it to your answer for parts (a), (b), and (c). For the third part of the problem, we will use hill climbing, which employs numerical differentiation. The goal of the hill-climbing algorithm is to maximize some continu- ously differentiable function h(2). The algorithm works as follows: Given a point 2, consider increasing 2 by a small amount say 0.001. Approximate the effect of increasing - on f via the differential dh =W(z) x 0.001, If dh > 0, then increase - to 3 +0.001. If dh 0, then increase - to 3 +0.001. If dh