Web Chapter C
Linear-Programming Applications
1. The fixed per-unit profit contribution coefficients of the objective function in a linear
programming problem imply the following economic assumptions except:
a. selling prices per unit of the products (outputs) are constant
b. constant returns to scale in the production process
c. buying prices per unit of the resources (inputs) are proportional to the amount purchased
d. both b and c
e. both a and c
2. Which of the following statements concerning dual variables is (are) true?
a. Dual variables are obtained automatically in an algebraic solution of a linear
programming problem.
b. Dual variables are similar to the artificial variables used in the Langrange Multiplier
technique.
c. A dual variable indicates how much the objective function will change if one additional
unit of a given resource is made available, provided that the increase in the resource does
not shift the optimal solution to another corner of the feasible solution space.
d. a and c
e. a, b, and c
3. If the primal linear programming problem has two variables and four constraints (excluding
the non-negativity constraints), the corresponding dual linear programming problem will
have ___________________.
a. two variables and four constraints
b. four variables and two constraints
, c. two variables and two constraints
d. four variables and four constraints
e. none of the above
4. A dual variable equal to zero in the optimal solution to a profit-maximization linear
programming problem indicates that the objective function will not increase if an additional
unit of the given resources is made available.
a. true
b. false
5. An optimal solution of a linear programming problem always lies on the boundary of the
feasible solution space.
a. true
b. false
6. A primal linear programming problem has multiple optimal solutions if it contains two or
more variables.
a. true
b. false
7. An optimal solution of a linear programming problem always occurs at one (or more) of the
corner points of the feasible solution space.
a. true
b. false
8. Slack variables are given coefficients of ______ in the objective function.
a. +1
b. 0
c. 1
, d. +.00001
e. none of the above
9. In a maximization linear programming problem, the ________ variables represent the
difference between the right-hand sides and left-hand sides of less than or equal to ()
inequality constraints.
a. dual
b. slack
c. primal
d. both a and b
e. none of the above
10. In a minimization linear programming problem, the ________ variables are subtracted from
the greater than or equal to () inequality constraints in order to convert these constraints to
equalities.
a. dual
b. primal
c. surplus
d. both a and b
e. both a and c
11. A computer solution of large-scale linear programming problems typically employs a
procedure (or variation of the procedure) known as the method.
a. least squares
b. analysis of variance
c. simplex
d. primal/dual
e. none of the above
, 12. variables are given coefficients of zero in the objective function of a
minimization linear programming problem.
a. Primal
b. Dual
c. Surplus
d. Dummy
e. none of the above
Linear-Programming Applications
1. The fixed per-unit profit contribution coefficients of the objective function in a linear
programming problem imply the following economic assumptions except:
a. selling prices per unit of the products (outputs) are constant
b. constant returns to scale in the production process
c. buying prices per unit of the resources (inputs) are proportional to the amount purchased
d. both b and c
e. both a and c
2. Which of the following statements concerning dual variables is (are) true?
a. Dual variables are obtained automatically in an algebraic solution of a linear
programming problem.
b. Dual variables are similar to the artificial variables used in the Langrange Multiplier
technique.
c. A dual variable indicates how much the objective function will change if one additional
unit of a given resource is made available, provided that the increase in the resource does
not shift the optimal solution to another corner of the feasible solution space.
d. a and c
e. a, b, and c
3. If the primal linear programming problem has two variables and four constraints (excluding
the non-negativity constraints), the corresponding dual linear programming problem will
have ___________________.
a. two variables and four constraints
b. four variables and two constraints
, c. two variables and two constraints
d. four variables and four constraints
e. none of the above
4. A dual variable equal to zero in the optimal solution to a profit-maximization linear
programming problem indicates that the objective function will not increase if an additional
unit of the given resources is made available.
a. true
b. false
5. An optimal solution of a linear programming problem always lies on the boundary of the
feasible solution space.
a. true
b. false
6. A primal linear programming problem has multiple optimal solutions if it contains two or
more variables.
a. true
b. false
7. An optimal solution of a linear programming problem always occurs at one (or more) of the
corner points of the feasible solution space.
a. true
b. false
8. Slack variables are given coefficients of ______ in the objective function.
a. +1
b. 0
c. 1
, d. +.00001
e. none of the above
9. In a maximization linear programming problem, the ________ variables represent the
difference between the right-hand sides and left-hand sides of less than or equal to ()
inequality constraints.
a. dual
b. slack
c. primal
d. both a and b
e. none of the above
10. In a minimization linear programming problem, the ________ variables are subtracted from
the greater than or equal to () inequality constraints in order to convert these constraints to
equalities.
a. dual
b. primal
c. surplus
d. both a and b
e. both a and c
11. A computer solution of large-scale linear programming problems typically employs a
procedure (or variation of the procedure) known as the method.
a. least squares
b. analysis of variance
c. simplex
d. primal/dual
e. none of the above
, 12. variables are given coefficients of zero in the objective function of a
minimization linear programming problem.
a. Primal
b. Dual
c. Surplus
d. Dummy
e. none of the above
