Riemann surface
matlab

Part I. For each statement, indicate $”+”=$ true or “o” $=$ false.

1. A “pivot” in a nonbasic column of a tableau will make it a basic column.
$\mathrm{O}$ 2. If a zero appears on the right-hand-side of row $i$ of an LP tableau, then at the next iteration you cannot pivot in row $\mathrm{i}$.
O 3. A “pivot” in row $\mathrm{i}$ of the column for variable $\mathrm{X}_{\mathrm{j}}$ will increase the number of basic variables.

4. A basic solution of the problem “maximize cx subject to $\mathrm{Ax} \leq \mathrm{b}, \mathrm{x} \geq 0$ ” corresponds to a corner of the feasible region.

5. In a basic LP solution, the nonbasic variables equal zero.

Part II. Below are several simplex tableaus. Assume that the objective in each case is to be maximized. Classify each tableau by writing to the right of the tableau a letter $\mathbf{A}$ through $\mathbf{F}$, according to the descriptions below. Also circle the pivot element when specified.
(A) Nonoptimal, nondegenerate tableau with bounded solution. Circle a pivot element which would improve the objective.
(B) Nonoptimal, degenerate tableau with bounded solution. Circle an appropriate pivot element.
(C) Unique optimum.
(D) Optimal tableau, with alternate optimum. Circle a pivot element which would lead to another optimal basic solution.
(E) Objective unbounded (above).
(F) Tableau with infeasible basic solution.

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