Consider the following problem.

Maximize Z 6x1  8x2, subject to 5x1  2x2 20 x1  2x2 10 and x1  0, x2  0.

(a) Construct the dual problem for this primal problem.

(b) Solve both the primal problem and the dual problem graphically. Identify the CPF solutions and corner-point infeasible solutions for both problems. Calculate the objective function values for all these solutions.

(c) Use the information obtained in part

(b) to construct a table listing the complementary basic solutions for these problems.

(Use the same column headings as for Table 6.9.)

I

(d) Work through the simplex method step by step to solve the primal problem. After each iteration (including iteration 0), identify the BF solution for this problem and the complementary basic solution for the dual problem. Also identify the corresponding corner-point solutions.