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Rectangular slabs cast from $1020$ annealed steel are heated and flat$-$rolled to improve their metallurgical structure and reduce their thickness. The slabs are $1\mathrm{.}5m9m18cm$ with a density of $7590k\frac{g}{m^3}.$ After passing through a $5-$stand roughing mill, the rolled product will have a thickness of $3mm.$ Vertical rolls are used to prevent widening of the slabs so the width of the finished product does not change; however, the density of the finished product increases by $0\mathrm{.}1\%.$

a$)$ What is the length of the final rolled product?

We want the first stand in the $5-$stand roughing mill to reduce the thickness of the slab from $18cm$ to $16cm.$ The roll's diameter is $600mm$ and it rotates at $75rpm.$ The motor driving the roll has $8,000kW$ of power with an efficiency of $75\%.$ For $1020$ annealed steel, $K=745$MPa and $n=0\mathrm{.}20.$

b$)$ Will you be able to perform this rolling job in one pass $($i$.$e$.,$ reduce from $18cm$ to $16cm$ in one pass through the rolls$)?$

c$)$ Will you be able to perform this rolling job in two passes $($with equal reduction in every pass$)?$

Justify your answer with calculations.