Consider the following multiobjective problem: Note that the decision variables must be nonnegative and integer. They do not need to be binary 0 or 1 ð Þ variables (a) Find the solution that minimizes...

Consider the following multiobjective problem:

Note that the decision variables must be nonnegative and integer. They do not need to be binary 0 or 1 ð Þ variables

(a) Find the solution that minimizes Z₁
first and then, from among the solutions that do so, minimizes Z₂
second. What weights on Z₁
and Z₂
must you use to find the solution?

(b) Find the solution that minimizes Z₂
first and then, from among the solutions that do so, minimizes Z₁
second. What weights on Z₁
and Z₂
must you use to find the solution?

(c) Use the weighting method described in the text to find all the noninferior points you can using this approach. Clearly identify the weights on Z₁
and Z₂
that you must use to find each solution.

(d) Carefully plot the constraints, the feasible region, and the objective functions. Did the weighting approach find all of the noninferior points? If not, identify all noninferior solutions not found in part (c).