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 Subject to: Constraint 1 Constraint 2 5000 X1 + 7000X2 + 9000X3 X1 + X2 + X3 2 -X1 + X2 50 25,000 X1 + 32,000 X2 + 29,000 X3S 62,000 16 X1 + 14 X2 + 19 X3 36 all variables = 0 or 1 (budget limit) (resource limitation) 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. Suppose you wish to add a constraint that stipulates that both alternative 2 and alternative 3 must be selected, or neither can be selected. How would this constraint be written? X22 X3 233 o X2 + X3 = 1 O X2 = X3 A city is reviewing the location of its fire stations. The city is made up of a number of districts, as illustrated below. A fire station can be placed in any district and is able to handle the fires for both its neighborhood and any adjacent neighborhood. The objective is to minimize the number of fire stations used. 1 2 5 3 4 6 7 At least three fre stations are needed to cover the city False