Assuming that $Z$ and $W$ values are decision variables, determine whether each of the following

mathematical programs is best described as a linear program $($LP$),$ a non$-$linear program $($NLP$),$

an integer linear program $($ILP$),$ or an integer nonlinear program $($INLP$),$ and briefly explain why.

$(1$ points$)$

a$)$

max,$3z_1+14z_2+7z_3$

$s.t.10z_1+5z_2+18z_{3}25$

$,z_j=0or1,j=1,$dots,$3$

b$)$

max,$44z_1+2z_2+98z_3$

$s.t.12z_1+92z_2+88z_{3}95$

$,z_{j}0,j=1,$dots,$3$

c$)$

min,$7z_1{z}_2+17z_2{z}_3+27z_1{z}_3$

$s.t.{\displaystyle \underset{j=1}{\overset{3}{}}}{z}_j=2$

$,z_{j}0,j=1,$dots,$3$

d$)$

max,${\displaystyle \underset{j=1}{\overset{10}{}}}{}_j{w}_j$

$s.t.(w_1{)}^2+w_2{w}_{3}14$

$,w_1,w_2,w_{3}1,w_2$ integer