Consider the following LP problem:
MAX: 2X1 + 4X2
Subject to: -X1 + 2X2 ≤ 8
X1 + 2X2 ≤ 12
X1 + X2 ≥ 2
X1, X2 ≥ 0
a. Use slack variables to rewrite this problem so that all its constraints are “equal to” constraints.
b. Identify the different sets of basic variables that might be used to obtain a solution to the problem.
c. Of the possible sets of basic variables, which lead to feasible solutions and what are the values for all the variables at each of these solutions?
d. Graph the feasible region for this problem and indicate which basic feasible solution corresponds to each of the extreme points of the feasible region.
e. What is the value of the objective function at each of the basic feasible solutions?
f. What is the optimal solution to the problem?
g. Which constraints are binding at the optimal solution?