$28$ Consider the following two LPs:

max $==$ c$1$x $+$ C$2$X$2$

s$\mathrm{.}1.$

$411$x$1+912$x$2=$ bi

$($LP $1)$

a$21$x$1+422$x$2=$ b$2422$x$2$b$2$

max $=100$cpx$,+100$cx

s$.$t

X$1,$ X$20$

b$1$

$($LP $2)$

b$2$

X$1,$ X $=0$

$100$a$,$ x$+100$a$12$

$100$a$2$x$+100$ax$2$

Suppose that BV $=\{$x$1,$ x$2\}$ is an optimal basis for both LPs$,$ and the optimal solution to LP $1$ is x$1$

$50,$ x$2500550.$ Also suppose that for LP $1,$ the shadow price of $100$ Find the optimal

both Constraint $1$ and Constraint $23$ solution to LP $2$ and the optimal solution to the dual of LP $2.($Hint: If we multiply each number in a matrix by $100,$ what happens to B$?)$