Assignment:
Consider the following linear programming problem:
Minimize Z = 2x1 - x2
Subject to -2x1 +x2 ≤ 20 (Constraint 1)
x1 +x2 ≤ 30 (Constraint 2)
x1 +2x2 ≥ 20 (Constraint 3)
x2 ≥ 0
x1 unconstrained in sign
Let the slack of constrain (1) and (2) be x3 and x4, respectively, and the surplus of constraint (3) be x5.
a) Consider decreasing the right hand side of constraint (3) from its current value of 20. Find the critical value of the right hand side of constraint (3) beyond which constraint (3) becomes redundant.
b) Construct the intial basic solution by adding artifical variables and making the necessary variable transformations so that you can apply the Big-M method to the problem. Fill-in the (0) iteration tableau. Indicate the entering and leaving variable and performa a single Big-M iteration (1). Write the resulting basic solution (all variables with values) of iteration (1) and indicate whether it is feasible or infeasible to the problem.
Z = 22.1-2.2