Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Algebraic methods such as the simplex method are used to solve
a. | nonlinear programming problems. | b. | any size linear programming
problem. | c. | programming problems under uncertainty. | d. | graphical
models. |
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2.
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The basic solution to a problem with three equations and four variables would
assign a value of 0 to
a. | 0 variables. | b. | 1 variable. | c. | 3
variables. | d. | 7 variables. |
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3.
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A basic solution and a basic feasible solution
a. | are the same thing. | b. | differ in the number of variables allowed to be
zero. | c. | describe interior points and exterior points, respectively. | d. | differ in their
inclusion of nonnegativity restrictions. |
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4.
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When a set of simultaneous equations has more variables than constraints,
a. | it is a basic set. | b. | it is a feasible set. | c. | there is a unique
solution. | d. | there are many solutions. |
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5.
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Unit columns are used to identify
a. | the tableau. | b. | the c row. | c. | the b
column. | d. | the basic variables. |
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6.
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Which of the following is not a step that is necessary to prepare a linear
programming problem for solution using the simplex method?
a. | formulate the problem. | b. | set up the standard form by adding slack and/or
subtracting surplus variables. | c. | perform elementary row and column
operations. | d. | set up the tableau form. |
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7.
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A minimization problem with four decision variables, two
greater-than-or-equal-to constraints, and one equality constraint will have
a. | 2 surplus variables, 3 artificial variables, and 3 variables in the
basis. | b. | 4 surplus variables, 2 artificial variables, and 4 variables in the
basis. | c. | 3 surplus variables, 3 artificial variables, and 4 variables in the
basis. | d. | 2 surplus variables, 2 artificial variables, and 3 variables in the
basis. |
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8.
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In the simplex method, a tableau is optimal only if all the cj - zj values are
a. | zero or negative. | b. | zero. | c. | negative and
nonzero. | d. | positive and nonzero. |
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9.
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When there is a tie between two or more variables for removal from the simplex
tableau,
a. | post-optimality analysis is required. | b. | their dual prices will be
equal. | c. | converting the pivot element will break the tie. | d. | a condition of
degeneracy is present. |
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10.
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An alternative optimal solution is indicated when in the simplex tableau
a. | a non-basic variable has a value of zero in the cj - zj row. | b. | a basic variable has a positive value in the
cj - zj row. | c. | a basic variable has
a value of zero in the cj - zj
row. | d. | a non-basic variable has a positive value in the cj - zj row. |
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