Problem $8$: A company using a level production policy has the following demand for six periods:

$\backslash$table$[[$Period$,$Demand$],[1,8],[2,6],[3,14],[4,6],[5,9],[6,5]]$

With a zero starting inventory balance, determine the following:

a$.$ The level production rate that will result in a zero iriventory balance after period $6.$

b$.$ The inventory and back orders per period with the production rate in period $4.$

c$.$ The level production rate that would eliminate back orders.