Review Questions 1593.8 What is a basis?
3.9 What is a pivot operation?3.10 What is the difference between a convex polyhedron and a convex polytope?
3.11 What is a basic degenerate solution?
3.12 What is the difference between the simplex algorithm and the simplex method?
3.13 How do you identify the optimum solution in the simplex method?
3.14 Define the infeasibility form.
3.15 What is the difference between a slack and a surplus variable?
3.16 Can a slack variable be part of the basis at the optimum solution of an LP problem?
3.17 Can an artificial variable be in the basis at the optimum point of an LP problem?
3.18 How do you detect an unbounded solution in the simplex procedure?
3.19 How do you identify the presence of multiple optima in the simplex method?
3.20 What is a canonical form?
3.21 Answer true or false:
(a)The feasible region of an LP problem is always bounded.
(b)An LP problem will have infinite solutions whenever a constraint is redundant.
(c)The optimum solution of an LP problem always lies at a vertex.
(d)A linear function is always convex.
(e)The feasible space of some LP problems can be nonconvex.
(f)The variables must be nonnegative in a standard LP problem.
(g)The optimal solution of an LP problem can be called the optimal basic solution.
(h)Every basic solution represents an extreme point of the convex set of feasible solu-
tions.
(i)We can generate all the basic solutions of an LP problem using pivot operations.
(j)The simplex algorithm permits us to move from one basic solution to another basic
solution.
(k)The slack and surplus variables can be unrestricted in sign.
(l)An LP problem will have an infinite number of feasible solutions.
(m)An LP problem will have an infinite number of basic feasible solutions.
(n)The right-hand-side constants can assume negative values during the simplex proce-
dure.
(o)All the right-hand-side constants can be zero in an LP problem.
(p)The cost coefficient corresponding to a nonbasic variable can be positive in a basic
feasible solution.
(q)If all elements in the pivot column are negative, the LP problem will not have a
feasible solution.
(r)A basic degenerate solution can have negative values for some of the variables.
(s)If a greater-than or equal-to type of constraint is active at the optimum point, the
corresponding surplus variable must have a positive value.
(t)A pivot operation brings a nonbasic variable into the basis.