1. Given f(x. y) =2x + 3y and the constraint g(x. y)= 17 + 913 - 36 -0 (a) Carefully draw several level curves for f (x. y). (You may use your own graph paper if you like). (b) Carefully draw g(x. y) =0 on the same grid. (c) Draw several gradient vectors of f (t. y). (d) Draw several gradient vectors of g (x. y) on the level curve where g ( x. y) - 0. (Focus on direction and relative size, they are too long to fit on the grid.) 2 (e) Use your graph to estimate the point(s) at which global maximum values occur for f(r. y) subject to g(x, y), and estimate the maximum value(s). This estimate comes from your graph! Do this before part (g)! You should be considering the theory of when a max will occur on gas discussed in the lecture. (f) Use your graph to estimate the point(s) at which global minimum values occur for f(x. y) subject to g(x, y), and estimate the minimum value(s). (g) Determine, exactly, the global maximum and minimum points and their corresponding functional values. How close were you in parts (e) and (f)