Plach Ataman is trying to choose players for the starting line up of the basketball team. The team consists of $15$ Players who have being to choose players for the starting line$-$uplent$)$ according to their bll$-$handling shooting rebounding, and defen rated $($on a scale of $1-$moderate to $3-$excellent$)$ according to theile equals to $1$ if player is chosen, O otherwise. $/$ E$/$ and $/=(0,2.6,8,10,20,21,22,25,26,37,40,41,44,72).$

Position

Ball$-$handling $($b$)$

Shooting $(5)$

Rebounding $(7)$

Defense $($d$)$

Height

No$.$

Player

$22\mathrm{.}00$ m

$2$

$0$

$2$

Kalaitzakis, Panagiotis

G$-$F

$2$

$21\mathrm{.}91$ m

$1$

Vildoza, Luca

$3$

$3$

$21\mathrm{.}94$ m

G

$1$

$6$

Moraitis, Dinitrios

$2$

$2$

G

$22\mathrm{.}15$ m

$3$

S

Balcerowski, Aleksander C

$2$

$1$

$21\mathrm{.}90$ m

$10$

Sloukas, Kostas

$1$

$3$

$3$

G

$12\mathrm{.}10$ m

$2$

$20$

Samoxdurov, Alexandros

F$-$C

$1$

$1$

$32\mathrm{.}06$ m

$3$

$21$

Papapetrou, Ioannis

$2$

F$-$C

$2$

$2$

$21\mathrm{.}93$ m

$22$

Grant, lerian

$3$

G

$11\mathrm{.}91$ m

$25$

Nunn, Kendrick

G

$3$

$3$

$1$

$32\mathrm{.}06$ m

$3$

$26$

Lessort. Mathias

C

$1$

$1$

$3$

$32\mathrm{.}08$ m$.$

$37$

Antetokounmpo, Kostas

F$-$C

$2$

$1$

$21\mathrm{.}98$ m

$40$

Grigoris. Marius

G$-$F

$2$

$3$

$22\mathrm{.}06$ m

$41$

Hermang$$mez$,$ Juancho

$2$

$3$

F

$2$

$22\mathrm{.}10$ m

$44$

Mitoglou, Dinos

F$-$C

$1$

$2$

$3$

$22\mathrm{.}07$ m

$2$

$72$

Mantzoukas, Lefteris

F

$1$

a$)$ The objective function maximizes the total defensive and ball handling ability of the team.

b$)$ At least $3$ members must be able to play guard, at least $2$ members must be able to play forward, and at least one member must be able to play center.

c$)$ If Mathias Lessort starts, Jerian Grant and Kendrick Nunn must both start.

d$)$ The average shooting level of the starting lineup must be at least $2.$

e$)$ If Kostas Antetokounmpo start, then Mathias Lessort cannot start,

f$)$ If Dinos Mitoglou starts, Luca Vildoza or Kostas Sloukas $($or both$)$ must start.