A company produces $2,000$ flash memories $($USB$)$ a day in its two shifts: $1,000$ USB in the first shift $(6$ am $-2$ pm$)$ and $1,000$ USB in the second shift $(2$ pm $-10$ pm$).$ The fixed manufacturing cost per day is $$4,000$ The total labor cost per shift is $$1,000$ The variable cost is $$2$ per USB produced a$.$ Compute the unit manufacturing cost $($cost per USB$).$ To increase its production to $3,000$ USB per day, the company is considering adding a nightshift $(10$ pm $-6$ am$)$: The labor cost for the night shift will be twice of the regular labor cost. $$ The fixed manufacturing cost per day will increase by $25\%.$ The variable cost will remain the same $($$$2$ per USB$).$ b$.$ Compute the average manufacturing cost per unit for a three$-$shift working day. $.$ c$.$ If the selling price of each USB is $$30$ each, is it profitable to introduce the night shift? Why?