A company wants to develop a level production. The beginning inventory is $4.$ Demand for the next four periods is given in what follows.

What production rate per period will give a zero inventory at the end of period $18$

When and in what quantities will backorders occur?

What level production rate per period will avoid backorders? Then what will be the ending inventory in period $48$

If the cost of carrying inventory is $$5$ per unit per period and stockout cost $$50$ per unit, what will be the total cost of the plan developed in $4\mathrm{.}1)?$

What will be the cost of the plan developed in $4\mathrm{.}3)?$

Which is the better production plan between $4\mathrm{.}1)$ and $4\mathrm{.}3)?$ Explain why.

$\backslash$table$[[$Period $($Month$),1,2,3,4,$Total$],[$Forecast$,12,6,8,14,],[$Production $($Level$)],[$Ending inventory,$4,,,,,]]$