Table $10-3$

A company has decided $to$ use $o^{-1}$ integer programming $to$ help make some investment decisions. There

are three possible investment alternatives from which $to$ choose, but $ifitis$ decided that a particular

alternative $istobe$ selected, the entire cost $of$ that alternative will $be$ incurred $(i.e.,itis$ impossible $to$

build one$-$half $of$ a factory$).$ The integer programming model $isas$ follows:

Subject $to$: $X1+X2+X3\frac{?}{\text{l}\text{e}\text{q}3}$ Constraint $1$

$-X3+X2\frac{?}{\text{l}\text{e}\text{q}0}$ Constraint $2$

$50,000\frac{?}{1}+40,000\frac{?}{2}+35,000\frac{?}{3}100,000(budgetlimit)$

$20x1+23\frac{?}{2}+25X3550(wesourcelimitation)$

all variables $=0or1$

where $x1=1if$ altemative $1is$ selected, $0$ otherwise

$x2=1if$ altemative $2is$ selected, $0$ otherwise

$3=1if$ altemative $3is$ selected, $0$ otherwise

Solution $x1=0,x_2=1,x3=1,$ objective value $=15,000.$

Table $10-3$ presents $an$ integer programming problem. What $is$ the meaning $of$ Constraint $1?$

$If{x}_{1}is$ selected, $x_2$ and $x_3$ must also $be$ selected.

$At$ least three alternatives must $be$ selected.

$No$ more than three alternatives may $be$ selected.

$If{x}_{2}is$ selected, $x_1$ and $x_3$ must also $be$ selected. Table $10-3$

A company has decided $to$ use $o^{-1}$ integer programming $to$ help make some investment decisions. There

are three possible investment alternatives from which $to$ choose, but $ifitis$ decided that a particular

alternative $istobe$ selected, the entire cost $of$ that alternative will $be$ incurred $(i.e.,itis$ impossible $to$

build one$-$half $of$ a factory$).$ The integer programming model $isas$ follows:

where $x1=1if$ altemative $1is$ selected, $0$ otherwise

$x2=1if$ altemative $2is$ selected, $0$ otherwise

$x3=1if$ altemative $3is$ selected, $0$ otherwise

Solution $x1=0,x_2=1,x3=1,$ objective value $=15,000.$

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 $bein$ the third constraint?

$10,000$

$25,000$

$30,000$

$8000$