Determine the optimal solution for the following assignment problem.

Machine

$\backslash$table$[[$Machine$],[1,2,3,4],[15,17,13,5],[11,7,14,8],[9,11,25,9],[7,13,10,12]]$

Q$2)-$ Given the following LP model and its optimal solution.

MaxZ$=c_1{x}_1+c_2{x}_2+c_3{x}_3$

S$.$T$.$

$a_{11}{x}_1+a_{12}{x}_2+a_{13}{x}_3{b}_1$

$a_{21}{x}_1+a_{22}{x}_2+a_{23}{x}_3{b}_2$

$a_{31}{x}_1+a_{32}{x}_2+a_{33}{x}_3{b}_3$

$\backslash$table$[[$B$.$V$.,x_1,x_2,x_3,S_1,S_2,S_3,$Solution$],[Z,4,0,0,1,2,0,270],[x_2,-\frac{1}{4},1,0,\frac{1}{2},-\frac{1}{4},0,20],[x_3,\frac{3}{2},0,1,0,\frac{1}{2},0,46],[S_3,2,0,0,-2,1,1,4]]$

Compute the following,

a$)-$ The value of $b_1,b_2,$ and $b_3.$

b$)-$ The value of $c_1,c_2,$ and $c_3.$

c$)-$ The value of $a_{11},a_{21},$ and $a_{31}.$

d$)-$ The value of $a_{12},a_{22},$ and $a_{32}.$

e$)-$ The value of $a_{13},a_{23},$ and $a_{33}.$