Question $18$

$1pts$

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 $6000x1+50002+70003$

Subject $to$: $x1+x2+x33$

$,-x3+x20$

$,59,000x1+4Q,0002+35,0003100,000$

$,20x1+23x2+25x350$

all variables $=0or1$

Constraint $1$

Constraint $2$

$($budget limit$)$

$($resousce limitation$)$

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

$xZ=1$ if alternative $Z$ is selected, $0$ otherwise

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

Solution $x1=0,x=1,x3=1,$ 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 be in the third constraint?

$10,000$

$25,000$

$30,000$

$8000$