Relaxed Linear Programs

$1.$ Consider the integer program Max. $8$x $+24$y

S$.$t$.5$x $+30$y $<=90$

$2$x $9$y $<=8$

x$,$ y $>=0,$ integral.

$($a$)$ Write the relaxed linear program.

$($b$)$ Graph the feasible set for the relaxed linear program.

$$ The website desmos.com provides a graphing tool.

$$ To easily see the feasible set, it is better to graph the opposite inequalities. In this

way, the feasible set is the unshaded region of the graph.

$($c$)$ Use linear programming software to solve the relaxed linear program.

$($d$)$ Find an optimal solution to the original integer program by investigating integer$-$valued

feasible points near the solution to the relaxed linear program. answer all problems and show work please