In a given period, demand for an item is equally likely to be any value between 200 and 299 units. Each unit costs $85 and is sold for $110 each. Any unsold stock at the end of the period can be sold for $35 a unit. What is the optimal order quantity for the period

The optimal order quantity for the period is 233 units

Explanation:

As per given data

Cost  = $85

Price = $110

Residual value = $35

First we need to calculate the overage and underage cost of the item

Overage cost = Cost - Residual value

Overage cost = $85 - $35

Overage cost = $50

and

Underage cost = Price - Cost

Underage cost = $110 - $85

Underage cost = $25

Now determint the critical ratio

Critical ratio = Underage cost / ( Overage cost + Underage cost )

Critical ratio = $25 / ( $50 + $25 )

Critical ratio = 0.33333

AS demand is equally divided between 200 and 299, so the optimal order quantity will be

Optimal Order quantity = Lowest demand + Critical ratio ( Highest demand - Lowest demand )

Optimal Order quantity = 200 units + 0.33333 ( 299 units - 200 units )

Optimal Order quantity = 200 units + 33 units

Optimal Order quantity = 233 units