Question

Acme Distributors has an annual demand for an airport metal detector of 1,275 units. The cost of a typical detector to Acme is $355. Carrying cost is estimated to be 15% of the unit cost, and the ordering cost is $35 per order. If Karen Powell, the owner, orders in quantities of 340 or more, she can get a 5% discount on the cost of the detectors.

a. What is the optimal order quantity, given the following price breaks for purchasing the item?                            [ Select ]                       ["17.15", "40.94", "35.56", "42.00"]      

b. What price should Acme pay per unit? $                            [ Select ]                       ["337.15", "340.00", "355.00", "425.50"]      

c. What is the total cost at the optimal behavior? $                            [ Select ]                       ["454,895.04", "510,900.47", "444,890.50", "438,724.88"]      

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2. Which of the following actions is consistent with the use of level scheduling?                            [ Select ]                       ["use overtime to meet higher-than-average demand requirements", "vary production levels to meet demand requirements", "none of the options are true", "use inventory to meet demand requirements"]      

Answer 1

a. Optimal Order Quantity

Here

Demand = Annual Demand = 1275

Order Cost = $35

Holding Cost = 15% * $ Unit Cost = 15% * $355 = $53,25

Putting these values in the above equation

Optimal Order Quantity = 40.94;

b. as the order quantity is far less than 340 i.e. Discount Quantity. Hence per unit price would remain unchanged i.e. $355.00

c. Total Cost at Optimal Quantity = Total Price of the Units + Ordering Cost + Holding Cost.

Total Price = $355 * 1275 = $452625

Total Orders = Annual Requirements/ Optimal Quantity = 1275/40.94 = 31.14

Ordering Cost = $35 * Total Orders = $35*31.14 = $1090.02

Optimal Order Quantity has be hold as inventory hence Holding Cost = 15% * $355 * 40.94 = 2180.04

Total Cost = $452625 + $1090.02 + $2180.04 = $455895.06