$5.$ Dynamic Lot sizing $($computing$)$

Solve the following dynamic lot sizing problem: determine the order$/$production quantity in each

period and the level of inventory at the end of each period, using the following policies

$-$ EOQ

$-$ Silver$-$meal heuristic

$-$ Part$-$period balancing

$-$ Wagner$-$Whitin procedure

The demand over the six$-$month horizon is $(20,40,50,30,10,30).$ The order setup cost is $$100,$ if

the order is placed in the first three months, and the order setup cost is $$150$ if the order is placed

in the last three months. The holding cost per unit per month is $$2.$