Find and Plot the Feasible Region in Decision Space Engineering

please use excel if necessaryQUESTION 2
Consider the following multi-objective linear program:
𝑀𝑎𝑥 𝑍1 = 𝑥 + 𝑦
𝑀𝑖𝑛 𝑍2 = 0.5𝑥 + 𝑦
Subject to:
𝑥 + 𝑦 ≤ 10
𝑥 ― 𝑦 ≤ 6
𝑦 ≤ 8
𝑥,𝑦 ≥ 0
a. Find and plot the feasible region in decision space
b. Plot the corresponding feasible region in objective space. For each extreme point, indicate if it is
non-inferior or dominated
c. Use the constraint method to generate an approximation of the non-inferior set. Generate 6 non-
inferior solutions evenly spaced in terms of 𝑍1.
d. Use the weighting method to generate an approximation of the non-inferior set. Generate 6 non-
inferior solutions (they don’t have to be unique) evenly spaced in terms of the weighting of the two
objectives.