$5.[15$ pts$]$ True or False. Explain why or provide a counter$-$example.

a$.$ In the simplex algorithm, a variable that has just left the basis cannot reenter in the

very next iteration.

b$.$ In the simplex algorithm, a variable that has just entered the basis cannot leave in the

very next iteration.

c$.$ If we have a constraint in standard maximum form, and we multiply both the right$-$

hand side of each constraint by $k$ and multiply the constants in the objective function

by $k,$ the optimal solution is also multiplied by $k.$

d$.$ It is possible to construct a linear program in which every feasible point is optimal

e$.$ A degenerate LP always has multiple solutions that provide the same optimal valu$5$edde