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

question 81

Multiple Choice

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 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.
-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

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