This chapter has described the simplex method as applied to linear programming problems where the objective function is to be maximized. Section 4.6 then described how to convert a minimization problem to an equivalent maximization problem for applying the simplex method. Another option with minimization problems is to make a few modifications in the instructions for the simplex method given in the chapter in order to apply the algorithm directly.
(a) Describe what these modifications would need to be.
(b) Using the Big M method, apply the modified algorithm developed in part (a) to solve the following problem directly by hand. (Do not use your OR Courseware.)
Minimize Z = 3x1 + 8x2 + 5x3,
Subject to

and
x1 ‰¥ 0, x2 ‰¥ 0, x3 ‰¥ 0.

312 4x70 3x1 + 5x2 + 2x3 70