$($a$)$ A snack bar at a certain theme park sees a constant, deterministic, continuous demand of

$150$ cases per day. Replenishment orders are placed to a central warehouse located within the

theme park, with negligible lead time, and it costs $$10$ in labor costs to deliver an order to

the snack bar from the warehouse. It costs $$1\mathrm{.}20$ per case per day in refrigeration costs and

other holding costs to hold cases of food in inventory at the snack bar. Calculate the optimal

order quantity Q$$

$.$ How often should orders be plac