Answer:
a) 138 units
b) 17 units
c) 17 units
d) Total Cost = $353.35
Explanation:
Given:
Average pizzas delivered = 200
Charge of inventory holding = 30% of cost
Lead time = 7 days
Now,
a) Economic Order Quantity = ![\sqrt\frac{2\times\textup{Annual Demand}\times\textup{Cost per Order}}{\textup{Carrying cost}}](https://tex.z-dn.net/?f=%5Csqrt%5Cfrac%7B2%5Ctimes%5Ctextup%7BAnnual%20Demand%7D%5Ctimes%5Ctextup%7BCost%20per%20Order%7D%7D%7B%5Ctextup%7BCarrying%20cost%7D%7D)
also,
Annual Demand = 200 × 12 = 2400
Cost per Order = Cost of Box + Processing Costs
= 30 cents + $10
= $10.30
and, Carrying Cost = ![\frac{\textup{Total Inventory Cost}}{\textup{total annual demand}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7BTotal%20Inventory%20Cost%7D%7D%7B%5Ctextup%7Btotal%20annual%20demand%7D%7D)
=![\frac{\textup{Total Cost per order}\times\textup{Annual demand}\times\frac{25}{100}}{\textup{Annual demand}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7BTotal%20Cost%20per%20order%7D%5Ctimes%5Ctextup%7BAnnual%20demand%7D%5Ctimes%5Cfrac%7B25%7D%7B100%7D%7D%7B%5Ctextup%7BAnnual%20demand%7D%7D)
= ![\frac{\$10.30\times2400}\times\frac{25}{100}}{2400}](https://tex.z-dn.net/?f=%5Cfrac%7B%5C%2410.30%5Ctimes2400%7D%5Ctimes%5Cfrac%7B25%7D%7B100%7D%7D%7B2400%7D)
= $2.575
Therefore,
Economic Order Quantity = ![\sqrt\frac{2\times\textup{2400}\times\textup{10.30}}{\textup{2.575}}](https://tex.z-dn.net/?f=%5Csqrt%5Cfrac%7B2%5Ctimes%5Ctextup%7B2400%7D%5Ctimes%5Ctextup%7B10.30%7D%7D%7B%5Ctextup%7B2.575%7D%7D)
= 138.56 ≈ 138 units
b) Reorder Point
= (average daily unit sales × the lead time in days) + safety stock
= (![\frac{200}{30}\times7](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B30%7D%5Ctimes7)
= 46.67 ≈ 47 units
c) Number of orders per year = ![\frac{\textup{Annual Demand}}{\textup{Economic order quantity}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7BAnnual%20Demand%7D%7D%7B%5Ctextup%7BEconomic%20order%20quantity%7D%7D)
= ![\frac{\textup{2400}}{\textup{138}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextup%7B2400%7D%7D%7B%5Ctextup%7B138%7D%7D)
= 17.39 ≈ 17 units
d) Total Annual Cost (Total Inventory Cost)
= Ordering Cost + Holding Cost
Now,
The ordering Cost = Cost per Order × Total Number of orders per year
= $10.30 × 17
= $175.1
and,
Holding Cost = Average Inventory Held × Carrying Cost per unit
Average Inventory Held =
= 69
Carrying Cost per unit = $2.575
Holding Cost = 69 × $2.575 =
$177.675
Therefore,
Total Cost = Ordering Cost + carrying cost
= $175.1 + $177.675 = $353.35