The Rush Order's Doubtful Deadline

"Can you handle this rush order for $1,500$ cases of hairspray for one of our nonbrand customers?" asked the sales manager of a toiletries company one Friday afternoon. "It's got to be shipped by the end of the third week in March." The sales manager was speaking to Chico JuareZ, supervisor of the packaging department.

"I don't know for sure," said Chico. "Monday will be March $1,$ and the very best we can do while working a five$-$day week is $100$ cases a day."

"That's great," said the sales manager. "Three weeks at $500$ cases a week should allow you to make the deadline."

"Not so fast," said Chico, "I've got to check out all the possibilities before I can agree to that deadline."

When Chico took a look at his records, this is what he discovered:

a$.$ The packaging machine is due for an overhaul on the second weekend of March.

b$.$ Absenteeism runs very high in his department when employees have to work Friday nights during the high school basketball playoffs in March.

c$.$ The plant superintendent has recently issued an edict that prevents the department from working overtime.

d$.$ Past records show that unscheduled downtime for repairs on the packaging machine have been running about $10$ percent. This has cut down proportionately on scheduled production.

Should Chico commit himself to shipping this order at the end of the third week in March? If not, when would be a reasonably sure date? Be prepared to explain your reasoning and to show your calculations.