Unit $7$ Exercises

Chapter $11$:

$$ Problem $5$

$5.$ Consider the following mixed$-$integer linear program:

Max $2$x$1+3$x$2$

$4$x$1+9$x$2<=36$

$7$x$1+512=35$

xy$,$ x$2>=0$ and x$,$ integer

$*$ Graph the constraints for this problem. Indicate on your graph all feasible mixed$-$integer solutions.

$*$ Find the optimal solution to the LP Relaxation. Round the value of x$,$ down to find a feasible mixed$-$integer solution. Is this solution optimal? Why or why not?

$*$ Find the optimal solution for the mixed$-$integer linear program.