5. Linear Programs Consider the following linear program: mmmzik 2@ + a0 (13) st xp + 2z 2 (16) x; 20 (17) z2 20 (18) (a) Sketch the feasible region of the linear program as well as the 5-, 10-, and 15-level sets of the abjective function. HINT: Recall that for f : R R and R, the a-level set of f is defined as { R" : f() = a}. (b) Express the linear program in the following form: max 'F (19) FERn st. AT 0 (23) Specify the values of , , A, and b. HINT: Consider adding additional slack variables to the optimization problem. (d) List the extreme points or vertices of the feasible region of the linear program given by equations (13)(18). (e) Find the optimal value p* and the optimal point * = (x},x3) of the linear program given by equations (13)-(18). HINT: Recall that for a linear program with a bounded feasible region, at least one optimal point is a vertex of the feasible region