#$1.$ Consider the following LP$.$ Implement it on Excel and answer the following quesMons:

Solve the following LP using Excel;

Max z $=4$x$1+6$x$2+7$x$3+8$x$4$

s$.$t$.$ x$1+$ x$2+$ x$3+$ x$4=950($constraint $1)$

x$4>=400($constraint $2)$

$2$x$1+3$x$2+4$x$3+7$x$4<=4,600($constraint $3)$

$3$x$1+4$x$2+5$x$3+6$x$4<=5,000($constraint $4)$

x$1,$ x$2,$ x$3,$ x$4>=0$

$($a$)$ What is the opMmal value?

$($b$)$ What is the opMmal soluMon?

$($c$)$ Which constraints are binding?

$($d$)$ What is the opMmal value and opMmal soluMon is the RHS of constraint $1$ is increased

by $10$ units?

$($e$)($d$)$ What is the opMmal value and opMmal soluMon is the RHS of constraint $2$ is

decreased by $10$ units?