QUESTION 14
1 PTS
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:
$6000X_1 + 8000X_2 + 7000X_3$
$X_1 + X_2 + X_3 \le 3$
$-X_3 + X_2 \le 0$
$50000 X_1 + 40000 X_2 + 35000 X_3 \le 100000$
$20X_1 + 23X_2 + 25X_3 \le 50$
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
Constraint 1
Constraint 2
(budget limit)
(resource limitation)
SOLUTION $X_1 = 0, X_2 = 1, X_3 = 1$, OBJECTIVE VALUE = 15000.
TABLE 10-3 PRESENTS AN INTEGER PROGRAMMING PROBLEM. SUPPOSE YOU WISH TO ADD A CONSTRAINT
THAT STIPULATES THAT BOTH ALTERNATIVE 1 AND ALTERNATIVE 2 MUST BE SELECTED, OR NEITHER CAN BE
SELECTED. HOW WOULD THIS CONSTRAINT BE WRITTEN?
$X_1 + X_2 = 1$
$X_1 = X_2$
$X_1 \le X_2$
$X_1 = X_2$
