1.
Consider a capital budgeting example with five projects from which to select. Let 
x
1
 
=
 1 if project 
a
 is selected, 0 if not, for 
a
 
=
 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. 
Write the appropriate constraint for the following condition: Choose no fewer than 3 projects. 
 
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2.
Consider a capital budgeting example with five projects from which to select. Let 
x
1
 
=
 1 if project 
a
 is selected, 0 if not, for 
a
 
=
 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. 
Write the appropriate constraint for the following condition: If project 3 is chosen, project 4 must be chosen. 
 
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3.
Consider a capital budgeting example with five projects from which to select. Let 
x
1
 
=
 1 if project 
a
 is selected, 0 if not, for 
a
 
=
 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300, respectively. The budget is $450. 
Write the appropriate constraint for the following condition: If project 1 is chosen, project 5 must not be chosen. 
 
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4.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 
This problem requires two different kinds of decision variables. Clearly define each kind.  
 
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5.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 
Write the objective function. 
 
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6.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 
Write a constraint to ensure that if machine 4 is used and machine 1 will not be used. 
 
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7.
The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. 
Write a constraint that will ensure that Weithoff purchases exactly two machines.
 
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8.
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S
1
, S
2
, S
3
, S
4
, S
5
, S
6
, and S
7
. The restrictions are: 
 
Restriction 1. Evaluating sites S
1
 
and 
S
3
 will prevent you from exploring site S
7
.
 
 
Restriction 2. Evaluating sites S
2 
or
 S
4 
will prevent you from assessing site S
5
. 
 
Restriction 3. Of all the sites, at least 3 should be assessed. 
Assuming that S
i
 is a binary variable, write the constraint for the first restriction. 
 
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9.
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S
1
, S
2
, S
3
, S
4
, S
5
, S
6
, and S
7
. The restrictions are: 
 
Restriction 1. Evaluating sites S
1
 
and 
S
3
 will prevent you from exploring site S
7
. 
 
Restriction 2. Evaluating sites S
2 
or
 S
4 
will prevent you from assessing site S
5
. 
 
Restriction 3. Of all the sites, at least 3 should be assessed. 
Assuming that S
i
 is a binary variable, write the constraint(s) for the second restriction. 
 
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10.
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S
1
, S
2
, S
3
, S
4
, S
5
, S
6
, and S
7
. The restrictions are: 
 
Restriction 1. Evaluating sites S
1
 
and 
S
3
 will prevent you from exploring site S
7
. 
 
Restriction 2. Evaluating sites S
2 
or
 S
4 
will prevent you from assessing site S
5
. 
 
Restriction 3. Of all the sites, at least 3 should be assessed. 
Assuming that S
i
 is a binary variable, write the constraint for the third restriction. 
 
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11.
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation? 
 
12.
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S
1
, S
2
, S
3
, S
4
, S
5
, S
6
, and S
7
. The restrictions are: 
 
Restriction 1. Evaluating sites S
1
 
and 
S
3
 will prevent you from exploring site S
7
. 
 
Restriction 2. Evaluating sites S
2 
or
 S
4 
will prevent you from assessing site S
5
.
 
Restriction 3. Of all the sites, at least 3 should be assessed. 
Assuming that S
i
 is a binary variable, the constraint for the first restriction is :
 
13.
You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S
1
, S
2
, S
3
, S
4
, S
5
, S
6
, and S
7
. The restrictions are: 
 
Restriction 1. Evaluating sites S
1
 
and 
S
3
 will prevent you from exploring site S
7
. 
 
Restriction 2. Evaluating sites S
2 
or
 S
4 
will prevent you from assessing site S
5
. 
 
Restriction 3. Of all the sites, at least 3 should be assessed. 
Assuming that S
i
 is a binary variable, write the constraint(s) for the second restriction.