Table 10-2 Maximize Z = 34 X1 +43 X2 + 29 X3 Subject to: 5X1 + 4 X2 + 7 X3 s 50 1 X1 + 2 X2 + 2 X3 = 16 3 X1 + 4 X2 + 1 X3 = 9 all Xi are integer and non-negative Final Integer Solution: Z = 208 Decision Variable X1 X2 X3 Solution 1 0 6 According to Table 10-2, which presents a solution for an integer programming problem, at the optimal solution, how much slack exists in the third constraint? 0 9 5 6 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 s 2 Constraint 1 Constraint -X1 + X2 50 2 25,000 X1 + 32,000 X2 (budget +29,000 X3 s 62,000 limit) 16 X1 + 14 X2 + 19 (resource X3 S 36 limitation) all variables = 0 or 1 where X1 = 1 if alternative 1 is selected, O otherwise X2 = 1 if alternative 2 is selected, O otherwise X3 = 1 if alternative 3 is selected, O 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? 5000 3300 1000 8000