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.What is the meaning of Constraint 2?
A)Both alternatives 1 and 2 must be selected.
B)If alternative 2 is selected,alternative 1 must also be selected.
C)Either alternative 1 or alternative 2 must be selected.
D)No more than one alternative may be selected.
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.What is the meaning of Constraint 2?
A)Both alternatives 1 and 2 must be selected.
B)If alternative 2 is selected,alternative 1 must also be selected.
C)Either alternative 1 or alternative 2 must be selected.
D)No more than one alternative may be selected.
E)None of the above

Quizplus · Accepted Answer

Constraint 2 states that if alternative 2 is selected, then alternative 1 must also be selected. This is because the coefficient for X₁ in constraint 2 is negative, indicating that selecting alternative 2 alone would violate the constraint. Therefore, the company must also select alternative 1 to ensure that constraint 2 is satisfied.

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