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. 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? 1) 5000 2) 1000 3) 8000 4) Cannot be computed 5) 3300
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 aparticular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it isimpossible 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.
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?
1) 5000
2) 1000
3) 8000
4) Cannot be computed
5) 3300
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
