$($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$ fer 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 placed?