Consider the following LP:

Maximize z = x1 + 3x2

Subject To:

x1 + x2 <= 2

-x1 + x2 <= 4

x1 unrestricted

x2 >0

a. Determine all basic feasible solutions of the problem

b. Use direct substitution in the objective function to determine the best basic solution

c. Solve the problem graphically, and verify that the solution obtained in (c) is the optimum.