Question $13$

Table $10-1$

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 $70001+60002+80003$

Subject to: $x1+x2+x31($only $1$ may be chosen$)$

$300001+180002+400003100,000($budget limit$)$

$151+182+15350($resource limitation$)$

all variables $=0$ or $1$

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

$x_2=1$ if alternative $2$ is selected, $0$ otherwise

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

The optimal solution is $x1=0,x2=0,x3=1$

According to Table $10-1,$ which presents an integer programming problem, if the optimal solution is used, what would the value of the objective function be$?$

$13,000$

$8,000$

$21,000$

$15,000$