Question

25 Consider the multiobjective optimization mod- 2- el max XI max -3x x2 s.t. ri+ x2 4 rr20 (a) Compute graphically a solution that is optimal if only the first objective is considered. (b) Compute graphically a solution that is optimal if only the second objective is considered. (c) Discuss the conflict inherent in trying to maxi- mize both objectives at once.

Answer 1

A.

MAXIMIZE: Z = -3 X1 + 1 X2

-1 X1 + 1 X2 ≤ 4 1 X1 + 0 X2 ≤ 8

X1, X2 ≥ 0

B.

MAXIMIZE: Z = 1 X1 + 0 X2

-1 X1 + 1 X2 ≤ 4 1 X1 + 0 X2 ≤ 8

X1, X2 ≥ 0

So we see from graph that A is the solution for part A and B and C are solution for B.

C.

As we see from graph that A is the solution for part A and B and C are solution for B, it is not possible to have both maximized at the same time, hence it is not possible to have maximized at the same time.