The following chart representing the graphical solution of a math program is provided:

Identify the coordinates of the optimal solution by graphical inspection under these circumstances:

$($a $3$ pts$)$ It is a LP with OF $=$ min Z$.$

$($b $3$ pts$)$ It is an IP with x $1$ and x $2$ integer with OF $=$ Max Z$.$

$($c $3$ pts$)$ It is a MIP with x $1$ continuous and x $2$ integer with OF $=$ Max Z$.$

$($d $3$ pts$)$ It is a MIP with x $1$ continuous and x $2$ binary with OF $=$ min Z$.$

$($e $3$ pts$)$ It is a MIP with x $1$ binary and x $2$ continuous with OF $=$ Max Z$.$

$($f $5$ pts$)$ Solve the IP $($with x $1$ and x $2$ integer$)$ using Relaxation and Rounding with OF $=$ min Z$.($Identify the

LP relaxation optimal solution and the estimated IP optimal solution$)$

x$1$

x $2$

$246810$

$2$

$4$

$6$

$8$

$10$

$12$

$12$

increasing Z

A$(4\mathrm{.}6$; $5\mathrm{.}6)$

B$(6\mathrm{.}6$; $3\mathrm{.}4)$

C$(5\mathrm{.}5$; $0)$

D$(0$; $3\mathrm{.}2)$

O$(0$; $0)$