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$7000$ X$1+6000$X$2+8000$X$3$

Subject to:X$1+$ X$2+$ X$3<=1($only $1$ may be chosen$)$

$30000$X$1+18000$X$2+40000$X$3<=100,000($budget limit$)$

$15$ X$1+18$ X$2+15$ X$3<=50($resource limitation$)$

all variables $=0$ or $1$

whereX$1=1$ 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

The optimal solution is X$1=0,$ X$2=0,$ X$3=1$

In Table $10-1,$ which presents an integer programming problem, using the optimal solution means only one of the alternatives would be selected. How much slack is there in the third constraint?

Group of answer choices

$0$

$30$

$40$

$45$