Consider the following problem.
Maximize z = 3x1 + 2x2.
Subject to

and
x1 ‰¥ 0, x2 ‰¥ 0.

(a) Solve this problem graphically. Identify the CPF solutions by circling them on the graph.

(b) Identify all the sets of two defining equations for this problem. For each set, solve (if a solution exists) for the corresponding corner-point solution, and classify it as a CPF solution or corner-point infeasible solution.

(c) Introduce slack variables in order to write the functional constraints in augmented form. Use these slack variables to identify the basic solution that corresponds to each corner-point solution found in part (b).

(d) Do the following for each set of two defining equations from part (b): Identify the indicating variable for each defining equation. Display the set of equations from part (c) after deleting these two indicating (nonbasic) variables. Then use the latter set of equations to solve for the two remaining variables (the basic variables). Compare the resulting basic solution to the corresponding basic solution obtained in part (c).

(e) Without executing the simplex method, use its geometric interpretation (and the objective function) to identify the path (sequence of CPF solutions) it would follow to reach the optimal solution. For each of these CPF solutions in turn, identify the following decisions being made for the next iteration: (i) which defining equation is being deleted and which is being added; (ii) which indicating variable is being deleted (the entering basic variable) and which is being added (the leaving basic variable).

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