Table 10-1
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 (only 2 may be chosen)
25000X 1 + 32000X 2 + 29000X 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
The optimal solution is X 1 = 0,X 2 = 1,X 3 = 1
-In Table 10-1,which presents an integer programming problem,using the optimal solution means only two of the alternatives would be selected.How much slack is there in the third constraint?
A)0
B)3
C)33
D)36
E)None of the above

Question

Table 10-1
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 (only 2 may be chosen)
25000X 1 + 32000X 2 + 29000X 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
The optimal solution is X 1 = 0,X 2 = 1,X 3 = 1
-In Table 10-1,which presents an integer programming problem,using the optimal solution means only two of the alternatives would be selected.How much slack is there in the third constraint?
A)0
B)3
C)33
D)36
E)None of the above

Quizplus · Accepted Answer

The third constraint is 16*0 + 14*1 + 19*1 ≤ 36. The left side equals 33, so the slack is 36 - 33 = 3.

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