Sally's Bumpershoot Concern uses the Transportation $($i$.$e$.$ "Tableau", in French oooh laah laah$)$ method for production planning purposes.

Sally's costs of production are:

Regular production costs $$2/$unit

overtime production costs $$4/$unit

Subcontracted production costs $$10/$unit

Backordering costs $$4/$unit$/$quarter

Invetory costs $$3/$unit$/$quarter

Sally's capacity constraints are:

Regular production capacity: $2000$ units$/$qtr

Overtime production capacity: $1000$ units$/$qtr

Subcontracted production capacity: $3000$ units$/$qtr

The beginning inventory is $500$ units.

Quarterly demands are

Q$1-4500$

Q$2-5000$

Q$3-2000$

Go ahead and solve for the optimal production plan. How many units used during Q$1$ are produced after Q$1?[$That is$,$ how many units sold in Q$1$ are Backordered?$]$