Question 1 (25 pts): Target purchases room humidifiers produced by a supplier in
ID: 357840 • Letter: Q
Question
Question 1 (25 pts): Target purchases room humidifiers produced by a supplier in China. Target stores sell 10,000 humidifiers each year. Assume a constant demand rate. Each humidifier costs $10 and annual holding cost is 30 percent of the unit cost. Shipping company charges Target $700 as a fixed cost per shipment. a) (7 pts) What is the optimal order size for Target? b) (4 pts) How many orders does Target place per year when it uses optimal order size? c) (7 pts) Calculate the annual ordering (set up), holding, and purchase costs under the optimal order size? d) (7 pts) Suppose Target wants to decrease its optimal order size to 2000 units to decrease inventories To do so, by how much should Target reduce its fixed ordering (shipment) cost?Explanation / Answer
Annual demand, D = 10000
Holding cost, H = 10*0.3 = $ 3
Order (shipment) cost, S = $ 700
a) Optimal order size = SQRT(2*D*S/H) = SQRT(2*10000*700/3) = 2160
b) Number of orders per year = D/Q = 10000/2160 = 4.63 orders per year
c) Annual ordering cost = (D/Q)*S = (10000/2160)*700 = $ 3,240
Annual holding cost = (Q/2)*H = (2160/2)*3 = $ 3,240
Purchase cost = D*Cost = 10000*10 = $ 100,000
Total cost = 3240+3240+100000 = $ 106,480
d) Target order size = 2000
Equate order size to the optimal order quantity formula
SQRT(2*10000*S/3) = 2000
Solving it for S, we get,
S = 20002*3/(2*10000)
= $ 600
Therefore, Target should reduce its fixed ordering (shipment) cost (S) from $ 700 to 600 , which is a reduction of = 700-600 = $ 100
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