Problem $3(10$ marks$).$ Outdoor Fun sells lawn chairs. Annual demand is normally distributed, with mean

of $960$ chairs and variance of $3,072\mathrm{.}49.$ Outdoor Fun orders its chairs from its flagship store. It costs $$50$

to place an order, and the lead time is one month. Outdoor Fun estimates that each stockout causes a

loss of $$80$ in future goodwill. Outdoor fun pays $$30$ for each chair and sells it for $$40.$ The annual cost

of holding a chair in inventory is $$6.$

Determine the order quantity, the reorder point, and the safety stock under the assumption that all

demands are backordered.

Determine the order quantity, the reorder point, and the safety stock under the lost sales

assumption. The cost of a lost sale is $$90.$