Using the Wagner$-$Whitin algorithm work out the inventory policy for a business with a fluctuating weekly requirement over a complete $12$ months $(52$ weeks$).$

Weekly requirements for the product for the first $10$ weeks are as follows: $20,50,10,50,50,10,20,40,20,30.$

Every $10$ weeks the demand pattern repeats throughout the $12$ months.

Ordering cost is $$100$ per order

The carrying cost is $1\%$ of the unit cost per unit per week.

The unit cost is $$10$ per unit.

Considering a fixed lead time, calculate the optimal inventory policy using the Wagner$-$Whitin algo for the $52-$week period.