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 Constraint 1 -X1 + X2 ≤ 0 Constraint 2 25,000 X1 + 32,000 X2 + 29,000 X3 ≤ 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 Solution x1 = 1, x2 = 0, x3 = 1, objective value = 14,000. Suppose you wish to add a constraint that stipulates that both alternative 2 and alternative 3 must be selected, or neither can be selected. How would this constraint be written? 1) X2 = X3 2) X2 + X3 = 0 3) X2 ≤ X3 4) X2 + X3 = 1 5) X2 ≥ X3
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 Constraint 1
-X1 + X2 ≤ 0 Constraint 2
25,000 X1 + 32,000 X2 + 29,000 X3 ≤ 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
Solution x1 = 1, x2 = 0, x3 = 1, objective value = 14,000.
Suppose you wish to add a constraint that stipulates that both alternative 2 and alternative 3 must be selected, or neither can be selected.
How would this constraint be written?
1) X2 = X3
2) X2 + X3 = 0
3) X2 ≤ X3
4) X2 + X3 = 1
5) X2 ≥ X3
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