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
-According to Table 10-1,which presents an integer programming problem,if the optimal solution is used,how much of the budget would be spent?
A)$32,000
B)$29,000
C)$61,000
D)$62,000
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
-According to Table 10-1,which presents an integer programming problem,if the optimal solution is used,how much of the budget would be spent?
A)$32,000
B)$29,000
C)$61,000
D)$62,000
E)None of the above

Quizplus · Accepted Answer

The optimal solution selects alternatives 2 and 3. The costs are $32,000 and $29,000, respectively, totaling $61,000.

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