Consider the following problem.

Maximize Z  2x1  x2 4x3  3x4, subject to x1  x2  3x3  2x4 4 x1  x2 x3  x4  1 2x1  x2 x3  x4 2 x1  2x2  x3  2x4  2 and x2  0, x3  0, x4  0

(no nonnegativity constraint for x1).

(a) Reformulate this problem to fit our standard form for a linear programming model presented in Sec. 3.2.

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

(c) Using the two-phase method, construct row 0 of the first simplex tableau for phase 1.

C

(d) Use a computer package based on the simplex method to solve the problem.

I