A company has decided to use $01$ 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$3<=2$ Constraint $1$

$-$X$1+$ X$2<=0$ Constraint $2$

$25,000$ X$1+32,000$ X$2+29,000$ 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

Solve the problem using the Excel Template provided in Module $6$ Brightspace.

Table $10-3$ presents an integer programming problem. What is true about Constraint $1$ and the optimal objective function? PLEASE SOLVE IT IN EXCEL