(25 pts.) Consider the following problem.

Maximize Z = 2x1 + 5x2 + 3x3

s.t. x1 - 2x2 + 3x3 20

2x1 + 4x2 + x3 = 50

x1 + x2 + 3x3 4

x1 - x3 -1

and

x1, x2, x3 0

a. Reformulate this problem to fit our standard form (canonical form) for a linear programming model.

b. Using the Big M method, construct the complete first simplex table for the simplex method and identify the corresponding initial BF solution. Also identify the initial entering basic variable and the leaving basic variable.

c. What kind of a final simplex table would indicate an infeasible solution for this problem (in terms of basic variables) (explain in words)?