A company has decided to use binary 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 $5000$ X$1+7000$X$2+9000$X$3$

Subject to:

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

$25000$X$1+32000$X$2+29000$X$3<=62,000($budget limit$)$

$16$ X$1+14$ X$2+19$ X$3<=36($resource limitation$)$

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

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

According to the model above, which presents an integer programming problem, if the optimal solution is used, what would the value of the objective function be$?$

Group of answer choices

$12,000$

$21,000$

$2$

$16,000$