Table 10-3
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 X 1 + 7000X 2 + 9000X 3
Subject to: X 1 + X 2 + X 3 ≤ 2 Constraint 1
-X 1 + X 2 ≤ 0 Constraint 2
25,000 X 1 + 32,000 X 2 + 29,000 X 3 ≤ 62,000 (budget limit)
16 X 1 + 14 X 2 + 19 X 3 ≤ 36 (resource limitation)
all variables = 0 or 1
where X 1 = 1 if alternative 1 is selected,0 otherwise
X 2 = 1 if alternative 2 is selected,0 otherwise
X 3 = 1 if alternative 3 is selected,0 otherwise
Solution x 1 = 1,x 2 = 0,x 3 = 1,objective value = 14,000.
-Table 10-3 presents an integer programming problem.If the optimal solution is used,then only two of the alternatives would be selected.How much slack would there be in the third constraint?
A)1000
B)5000
C)3300
D)8000
E)None of the above

Question

Table 10-3
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 X 1 + 7000X 2 + 9000X 3 
Subject to: X 1 + X 2 + X 3 ≤ 2 Constraint 1
-X 1 + X 2 ≤ 0 Constraint 2
25,000 X 1 + 32,000 X 2 + 29,000 X 3 ≤ 62,000 (budget limit)
16 X 1 + 14 X 2 + 19 X 3 ≤ 36 (resource limitation)
all variables = 0 or 1
where X 1 = 1 if alternative 1 is selected,0 otherwise
X 2 = 1 if alternative 2 is selected,0 otherwise
X 3 = 1 if alternative 3 is selected,0 otherwise
Solution x 1 = 1,x 2 = 0,x 3 = 1,objective value = 14,000.
-Table 10-3 presents an integer programming problem.If the optimal solution is used,then only two of the alternatives would be selected.How much slack would there be in the third constraint?
A)1000
B)5000
C)3300
D)8000
E)None of the above

Quizplus · Accepted Answer

The Answer of Table 10-3
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 X 1 + 7000X 2 + 9000X 3 
Subject to: X 1 + X 2 + X 3 ≤ 2 Constraint 1
-X 1 + X 2 ≤ 0 Constraint 2
25,000 X 1 + 32,000 X 2 + 29,000 X 3 ≤ 62,000 (budget limit)
16 X 1 + 14 X 2 + 19 X 3 ≤ 36 (resource limitation)
all variables = 0 or 1
where X 1 = 1 if alternative 1 is selected,0 otherwise
X 2 = 1 if alternative 2 is selected,0 otherwise
X 3 = 1 if alternative 3 is selected,0 otherwise
Solution x 1 = 1,x 2 = 0,x 3 = 1,objective value = 14,000.
-Table 10-3 presents an integer programming problem.If the optimal solution is used,then only two of the alternatives would be selected.How much slack would there be in the third constraint?
A)1000
B)5000
C)3300
D)8000
E)None of the above

Table 10-3 a Company Has Decided to Use 0−1 Integer Programming to Programming