An industrial plant needs to make $100,000$ parts per month to meet demand. Each month

contains $20$ working days, each of which allows for $3$ separate $8$ hour shifts.

$($a$)$ If a worker can produce $10$ parts$/$hour$,$ how many workers are needed on each shift? $(3$ marks$)$

$($b$)$ If material costs are $$\frac{10}{?}$ part, capital costs are $$100,000$ and labor costs are $$\frac{10}{?}$ hour, what is

the multifactor productivity of the plant? $(3$ marks$)$