A machine can produce $80$ pieces in three hours but with five scraps.

To produce $4500$ pieces with two machines:

a$.$ In one week $(5$ business days$),$ how many hours a day should we run both machines?

Hint: First, find out how many pieces two machines can produce in one hour $($productivity$).$ Next, divide the total amount of work by this value to find out how many hours are required to complete the task. Finally, divide the total hours by $5$ days to arrive at the answer.

b$.$ If we work only $7\mathrm{.}5$ hours a day, how many business days should we run this machine?

Hint: You know the total time required from the question $($a$)$ above. Divide that value by daily working time to arrive at the answer.

c$.$ Which option $($a$)$ or $($b$)$ do you prefer? Why?

d$.$ If your customer requests the delivery in $8$ days but the maximum daily operating time for a machine is limited to $10$ hours, what alternative solutions can you suggest to your customer?

Hint: You can propose two alternatives: $(1)$ Late delivery and $(2)$ Less quantity in $8$ days. You need to calculate the additional time you need and the total quantity you can produce in $8$ days.