##### Question

In: Operations Management

# Joe's Drones is attempting to minimize total inventory cost and maximize profits this year. Each drone...

Joe's Drones is attempting to minimize total inventory cost and maximize profits this year. Each drone costs Joe $100 to buy and he sells them for$150 each. Joe’s mom helps with the purchasing and ordering and he pays her $100 for every order she places. Joe leases warehouse space from a friend where he can store his inventory and he pays$2.50 per month for each board that he has to store to use this space.

Drones are a hot item and Joe expects to sell 2,500 of them this year. He is currently ordering once a month, but he thinks that he can save money if he optimizes his order quantity.

a) If Joe continues to order once a month this year, what will his Total Annual Cost of Inventory be?

b) Assuming Joe sells everything that he orders, what will his annual profit be if he continues to order once a month

c) What quantity should Joe to order that would minimize Total Cost of Inventory (not Total Cost - the is Inventory only)?

d) How much will Joe’s annual profit change if he orders based on the EOQ rather than ordering once a month?

## Solutions

##### Expert Solution

1. Annual demand = 2500

Order quantity if it is ordered once a month = 2500 / 12 = 208.33

Annual unit inventory holding cost = $2.50 / month x 12 months =$30

Ordering cost =$100 per order Annual ordering cost = Ordering cost x Number of orders = Ordering cost x Number of orders =$100 x 12 = $1200 Annual inventory holding cost = Annual unit inventory holding cost x average inventory =$30 x Order quantity/ 2

= $30 x 208.33/2 =$3124.95

Therefore, total annual cost of inventory

= annual ordering cost + annual inventory holding cost

= $1200 +$3124.95

= $4324.95  TOTAL ANNUAL COST OF INVENTORY =$4324.95
1. Annual profit for Joe

= Annual demandx ( Selling price – Purchase price ) – total annual cost of inventory

= 2500 x ( 150 – 100 ) – 4324.95

= $2500 x 50 -$4324.95

= $125000 -$4324.95

= $120675.05  ANNUAL PROFIT FOR JOE =$120675.05
1. The economic order quantity that should minimize total cost of inventory

= Square root ( 2 x Annual orderingcost x Annual demand/ Annual unit holding cost )

= Square root ( 2 x 100 x 2500 /30 )

= 129.09 ( 129 rounded to nearest whole number )

 JOE SHOULD ORDER 129 DRONES
1. Annual ordering cost = Ordering cost x Number of orders = Ordering cost x Annual demand/Order quantity = $100x 2500/129 =$1937.98

Annual inventory holding cost = Annual unit holding cost x Average inventory = Annual inventory holding cost x Order quantity /2 = $30 x 129/2 =$1935

Total annualinventory related cost = $1937.98 +$1935 = $3872.98 Reduction in inventory related cost = Annual inventory related cost ( for ordering once a month ) – annual inventory related cost ( order quantity = 129 drones ) =$4324.95 - $3872.98 =$451.97

With reduction in inventory related cost by $451.97, profit will increase by$451.97

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