$.$ A company wants to develop a level production plan. The beginning inventory is

zero. Demand for the next four periods is given in what follows.

a$.$ What production rate per period will give a zero inventory at the end of period $4?$

b$.$ When and in what quantities will backorders occur?

c$.$ What level production rate p If the cost of carrying inventory is $$60$ per unit per period and stockout cost $$500$ per

unit, what will be the cost of the plan developed in problem $2\mathrm{.}9$a$?$ What will be the

cost of the plan developed in $2\mathrm{.}9$c$?$