Consider the following linear program: max x1,x2R 2x1 3x2 (13) s.t. x1 2x2 8 (14) x1 x2 2 (15) x2 x1 2 (16) x1 0 (17) x2 0 (18) (a) Sketch the feasible region of the linear program as well as the 5-, 10-, and 15-level sets of the objective function. HINT: Recall that for f : R n 7 R and R, the -level set of f is defined as {x R n : f(x) = }. (b) Express the linear program in the following form: max xRn cx (19) s.t. Ax b (20) Specify the values of x, c, A, and b. (c) Express the linear program in the following form: min yRn cy (21) s.t. Ay = b (22) y 0 (23) Specify the values of y, c, A, and b. HINT: Consider adding additional slack variables to the optimization