a$)$ Report the optimal solution and the optimal value of the objective function. $(5$ marks$)$

b$)$ Calculate the amounts of slack$/$surplus and comment on what constraints are binding and

which ones are non$-$binding $(5$ marks$)$

c$)$ How much improvement in the objective function will we get if we increase the amount of

Steel by $12$ more units? $(5$ marks$)$

d$)$ Calculate the optimal value of the objective function $($according to this sensitivity report$)$ if

the coefficient of $x$ changes to $8$ and the coefficient of $y$ changes to $7$ simultaneously. Show

all the calculations $(5$ marks$)$