Question: Consider the following vector optimization problem: P: Max z1 = 8x1 + 1x2 Min z2 =x1 3x2 s.t. 4x1 + 15x2 60 7x1 + 11x2

Consider the following vector optimization problem:

P: Max z1 = 8x1 + 1x2

Min z2 =x1 3x2 s.t. 4x1 + 15x2 60

7x1 + 11x2 85

x1 2x2 <=0

x1, x2 <= 0.

(a) Plot the figure & show the improvement cone. (b) Determine the nondominated frontier in the graph.

(c) Given the weight combination (w1, w2) = (3, 1), determine the composite objective & optimize with LINDO/LINGO. Determine the objective values of the original (not the composite) objectives.

(d) Repeat (c) with the weight combinations (w1, w2) = (1, 3) & (w1, w2) = (1, 8).

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