dolution

Suppose the demand of a product in a retail store is 20000 per year and it occurs at a
constant rate. Placement of an order of this product to an outside supplier by the store is
$180. The super market authority has calculated the inventory holding cost per unit per
year as 95 cents.
a) Assume that deliberate shortages are allowed and fully backordered with a cost of $100
per backorder. Find the economic order quantity and the backorder quantity in this case
and also the annual minimal total cost of ordering, backordering and inventory holding.
b) If the production rate of processing the product is 30000 per year and the set up cost per
set up is $300 and the product is allowed to sell during production, then
i) Determine the Economic Production Quantity (EPQ)
ii) The number of deliveries per year and the cycle time of a lot
iii) The annual minimal total cost of set up and inventory holding of delivering EPQ.