In a goal programming problem with two goals at the same priority level, all the deviational variables are equal to zero in the optimal solution
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31) In a goal programming problem with two
goals at the same priority level, all the deviational variables are equal to
zero in the optimal solution. This means
A) there is no feasible solution to the
problem.
B) all goals are fully achieved.
C) nonlinear programming must be used to
solve this.
D) this problem was an integer programming
problem.
E) None of the above
32) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a profit of
$2,400 and goal number 2 was to have no idle time for workers in the factory.
The optimal solution to this problem resulted in a profit of $2,300 and no idle
time. What was the value for the objective function for this goal programming
problem?
A) 2300
B) 100
C) -100
D) 0
E) None of the above
33) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a profit of
$3,600 and goal number 2 was to have no wasted material. The optimal solution
to this problem resulted in a profit of $3,300 and no wasted material. What was
the value for the objective function for this goal programming problem?
A) 300
B) -300
C) 3300
D) 0
E) None of the above
34) In an integer programming problem, if
it is desired to have variable X be exactly twice the value of variable Y, the
constraint would be written
A) 2X + Y = 0.
B) X + 2Y = 0.
C) 2X – Y = 0.
D) X – 2Y = 0.
E) None of the above
Table 10-1
A company has decided to use 0-1 integer
programming to help make some investment decisions. There are three possible
investment alternatives from which to choose, but if it is decided that a particular
alternative is to be selected, the entire cost of that alternative will be
incurred (i.e., it is impossible to build one-half of a factory). The integer
programming model is as follows:
Maximize 5000 X1 + 7000X2 + 9000X3
Subject
to: X1 + X2 + X3 ? 2 (only
2 may be chosen)
25000X1 + 32000X2 + 29000X3 ? 62,000 (budget
limit)
16 X1 + 14 X2 + 19 X3 ? 36 (resource
limitation)
all variables = 0
or 1
where X1 = 1 if alternative 1 is selected, 0 otherwise
X2 = 1 if alternative 2 is selected, 0 otherwise
X3 = 1 if alternative 3 is selected, 0 otherwise
The optimal solution is X1 = 0, X2 = 1, X3 = 1
35) According to Table 10-1, which
presents an integer programming problem, if the optimal solution is used, what
would the value of the objective function be?
A) 21,000
B) 12,000
C) 16,000
D) 2
E) None of the above
36) According to Table 10-1, which
presents an integer programming problem, if the optimal solution is used, how
much of the budget would be spent?
A) $32,000
B) $29,000
C) $61,000
D) $62,000
E) None of the above
37) In Table 10-1, which presents an
integer programming problem, using the optimal solution means only two of the
alternatives would be selected. How much slack is there in the third
constraint?
A) 0
B) 3
C) 33
D) 36
E) None of the above
38) According to Table 10-1, which
presents an integer programming problem, the optimal solution is to select only
two of the alternatives. Suppose you wished to add a constraint that stipulated
that alternative 2 could only be selected if alternative 1 is also selected
(i.e., if alternative 1 is not selected, you may not select alternative 2;
however, you may select #1 and not select #2). How would this constraint be
written?
A) X1 = X2
B) X1 ? X2
C) X1 ? X2
D) X1 + X2 = 2
E) None of the above
Table 10-2
Maximize Z = 34 X1 + 43 X2 + 29 X3
Subject to: 5 X1 + 4 X2 + 7 X3 ? 50
1 X1 + 2 X2 + 2 X3 ? 16
3 X1 + 4 X2 + 1 X3 ? 9
all Xi are integer and non-negative
Final Integer
Solution: Z = 208
Decision
Variable Solution
X1 1
X2 0
X3 6
39) According to Table 10-2, which
presents a solution for an integer programming problem, at the optimal
solution, how much slack exists in the third constraint?
A) 0
B) 9
C) 5
D) 6
E) -1
40) We do not have a general method for
solving all types of ________ problems.
A) mixed-integer programming
B) 0-1 integer programming
C) goal programming
D) nonlinear programming
E) pure integer programming
41) A capital budgeting problem involving
the selection of possible projects under budget constraints is solved by which
of the following?
A) mixed-integer programming
B) 0-1 integer programming
C) goal programming
D) nonlinear programming
E) pure integer programming
42) A transportation problem is an example
of
A) a pure-integer programming problem.
B) a mixed-integer programming problem.
C) a zero-one integer programming problem.
D) a goal programming problem.
E) a nonlinear programming problem.
43) If we wish to develop a stock
portfolio wherein we maximize return and minimize risk, we would have to use
A) pure-integer programming.
B) goal programming.
C) zero-one integer programming.
D) mixed-integer programming.
E) nonlinear programming.
44) Another name for a 0-1 variable is
a(n) ________ variable.
A) either-or
B) binary
C) yes-no
D) quadratic
E) on-off
45) Terms that are minimized in goal
programming are called
A) deviational variables.
B) global variables.
C) decision variables.
D) minimization variables.
E) None of the above
46) The concept of a local optimum is
affiliated with which of the following?
A) mixed integer programming
B) integer programming
C) linear programming
D) nonlinear programming
E) goal programming
47) The concept of “satisficing”
is affiliated with which of the following?
A) mixed integer programming
B) integer programming
C) linear programming
D) nonlinear programming
E) goal programming
48) The following
.jpg”>
represents a:
A) goal programming problem.
B) mixed integer programming problem.
C) nonlinear programming problem.
D) 0-1 integer programming problem.
E) pure integer programming problem.
49) As part of a larger problem, you are
trying to determine whether or not to open a plant with a capacity of 10,000
units (using binary variable Y). You also define X as the number of units (if
any) produced at that plant. How will you ensure that Y will equal 1 if the
plant is open?
A) Y ? X
B) Y ? X
C) X + Y ? 2
D) X = 10000Y
E) X ? 10000Y
50) Which of the following is not
considered nonlinear programming?
A) nonlinear objective and nonlinear
constraints
B) linear objective with nonlinear
constraints
C) nonlinear objective with linear
constraints
D) binary decision variable with nonlinear
constraints
E) integer decision variable with linear
constraints31) In a goal programming problem with two
goals at the same priority level, all the deviational variables are equal to
zero in the optimal solution. This meansA) there is no feasible solution to the
problem.B) all goals are fully achieved.C) nonlinear programming must be used to
solve this.D) this problem was an integer programming
problem.E) None of the above32) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a profit of
$2,400 and goal number 2 was to have no idle time for workers in the factory.
The optimal solution to this problem resulted in a profit of $2,300 and no idle
time. What was the value for the objective function for this goal programming
problem?A) 2300B) 100C) -100D) 0E) None of the above33) A goal programming problem had two
goals (with no priorities assigned). Goal number 1 was to achieve a profit of
$3,600 and goal number 2 was to have no wasted material. The optimal solution
to this problem resulted in a profit of $3,300 and no wasted material. What was
the value for the objective function for this goal programming problem?A) 300B) -300C) 3300D) 0E) None of the above34) In an integer programming problem, if
it is desired to have variable X be exactly twice the value of variable Y, the
constraint would be writtenA) 2X + Y = 0.B) X + 2Y = 0.C) 2X – Y = 0.D) X – 2Y = 0.E) None of the aboveTable 10-1A company has decided to use 0-1 integer
programming to help make some investment decisions. There are three possible
investment alternatives from which to choose, but if it is decided that a particular
alternative is to be selected, the entire cost of that alternative will be
incurred (i.e., it is impossible to build one-half of a factory). The integer
programming model is as follows:Maximize 5000 X1 + 7000X2 + 9000X3Subject
to: X1 + X2 + X3 ? 2 (only
2 may be chosen) 25000X1 + 32000X2 + 29000X3 ? 62,000 (budget
limit) 16 X1 + 14 X2 + 19 X3 ? 36 (resource
limitation) all variables = 0
or 1where X1 = 1 if alternative 1 is selected, 0 otherwise X2 = 1 if alternative 2 is selected, 0 otherwise X3 = 1 if alternative 3 is selected, 0 otherwiseThe optimal solution is X1 = 0, X2 = 1, X3 = 135) According to Table 10-1, which
presents an integer programming problem, if the optimal solution is used, what
would the value of the objective function be?A) 21,000B) 12,000C) 16,000D) 2E) None of the above36) According to Table 10-1, which
presents an integer programming problem, if the optimal solution is used, how
much of the budget would be spent?A) $32,000B) $29,000C) $61,000D) $62,000E) None of the above37) In Table 10-1, which presents an
integer programming problem, using the optimal solution means only two of the
alternatives would be selected. How much slack is there in the third
constraint?A) 0B) 3C) 33D) 36E) None of the above38) According to Table 10-1, which
presents an integer programming problem, the optimal solution is to select only
two of the alternatives. Suppose you wished to add a constraint that stipulated
that alternative 2 could only be selected if alternative 1 is also selected
(i.e., if alternative 1 is not selected, you may not select alternative 2;
however, you may select #1 and not select #2). How would this constraint be
written?A) X1 = X2B) X1 ? X2C) X1 ? X2D) X1 + X2 = 2E) None of the aboveTable 10-2Maximize Z = 34 X1 + 43 X2 + 29 X3Subject to: 5 X1 + 4 X2 + 7 X3 ? 50 1 X1 + 2 X2 + 2 X3 ? 16 3 X1 + 4 X2 + 1 X3 ? 9 all Xi are integer and non-negativeFinal Integer
Solution: Z = 208 Decision Variable Solution X1 1 X2 0 X3 639) According to Table 10-2, which
presents a solution for an integer programming problem, at the optimal
solution, how much slack exists in the third constraint?A) 0B) 9C) 5D) 6E) -140) We do not have a general method for
solving all types of ________ problems.A) mixed-integer programmingB) 0-1 integer programmingC) goal programmingD) nonlinear programmingE) pure integer programming41) A capital budgeting problem involving
the selection of possible projects under budget constraints is solved by which
of the following?A) mixed-integer programmingB) 0-1 integer programmingC) goal programmingD) nonlinear programmingE) pure integer programming 42) A transportation problem is an example
ofA) a pure-integer programming problem.B) a mixed-integer programming problem.C) a zero-one integer programming problem.D) a goal programming problem.E) a nonlinear programming problem.43) If we wish to develop a stock
portfolio wherein we maximize return and minimize risk, we would have to useA) pure-integer programming.B) goal programming.C) zero-one integer programming.D) mixed-integer programming.E) nonlinear programming.44) Another name for a 0-1 variable is
a(n) ________ variable.A) either-orB) binaryC) yes-noD) quadraticE) on-off45) Terms that are minimized in goal
programming are calledA) deviational variables.B) global variables.C) decision variables.D) minimization variables.E) None of the above46) The concept of a local optimum is
affiliated with which of the following?A) mixed integer programmingB) integer programmingC) linear programmingD) nonlinear programmingE) goal programming47) The concept of “satisficing”
is affiliated with which of the following?A) mixed integer programmingB) integer programmingC) linear programmingD) nonlinear programmingE) goal programming48) The following .jpg”>represents a:A) goal programming problem.B) mixed integer programming problem.C) nonlinear programming problem.D) 0-1 integer programming problem.E) pure integer programming problem.49) As part of a larger problem, you are
trying to determine whether or not to open a plant with a capacity of 10,000
units (using binary variable Y). You also define X as the number of units (if
any) produced at that plant. How will you ensure that Y will equal 1 if the
plant is open?A) Y ? XB) Y ? XC) X + Y ? 2D) X = 10000YE) X ? 10000Y50) Which of the following is not
considered nonlinear programming?A) nonlinear objective and nonlinear
constraintsB) linear objective with nonlinear
constraintsC) nonlinear objective with linear
constraintsD) binary decision variable with nonlinear
constraintsE) integer decision variable with linear
constraints
