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 $60001+80002+70003$

Subject $to$: $1+2+33$

$,-3+20$

$,59,0001+40,0002+35,0003100,000$

$,201+232+25350$

all variables $=0or1$

Constraint $1$

Constraint $2$

$($budget limit$)$

$($resource limitation$)$

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

$x2=1$ if altemative $2$ is selected, $0$ otherwise X$3=1$ if altemative $3$ is selected, $0$ otherwise

Solution $x1=0,x2=1,x3=1,$ 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.