Consider the multiobjective LP max x1 max 2x1 + 2x2 s.t. 2x1 + x2 … 9 x1 … 4 x2 … 7 x1, x2 Ú 0

(a) Sketch the feasible space and contours where the first objective equals 3 and the second equals 14.

(b) Formulate a corresponding goal program seeking target levels 3 and 14 on the two objectives and minimizing the unweighted sum of goal violations.

(c) Explain why x = 12, 52 is optimal in the goal program of part

(b) by reference to the plot of part (a).