Bigbasket sells $550$ units per month of Sunsilk shampoo sachets. The unit cost of a sachet is Rs$\mathrm{.}7$ and the cost of placing an order is Rs$.44.$ Bigbasket uses an inventory carrying charge of $20\%$ per year. Determine the optimal order quantity, order frequency, and the annual cost of inventory management. If$,$ through automation of the purchasing process, the ordering cost can be cut to Rs$\mathrm{.}20,$ what will be the new economic order quantity, order frequency, and annual inventory management cost? Explain these results.

$[5]$