Millennium Liquors is a wholesaler of sparkling wines. Their most popular produc
ID: 358057 • Letter: M
Question
Millennium Liquors is a wholesaler of sparkling wines. Their most popular product is the French Bete Noire which is shipped directly from France. Weekly demand is for 50 cases. Millennium purchases each case for $105, there is a $300 fixed cost for each order (independent of the quantity ordered) and their annual holding cost is 25 percent What order quantity minimizes Millennium's annual ordering and holding costs? a. cases If Millennium chooses to order 275 cases each time, what is the sum of their annual ordering and holding costs? b. Round your answer to 2 decimal places.) If Millennium chooses to order 100 cases each time, what is the sum of the C. per case If Millennium is restricted to order in multiples of 50 cases (e.g., 50, 100, 150, holding costs? Millennium is offered a 5.00% discount if they purchase at least 1,000 cases. annual ordering and holding costs? d. etc.) how many cases should they order to minimize their annual ordering and cases e. If they decide to take advantage of this discount, what is the sum of their References eBook & Resources Learning Objective: 12-01 Evaluate optimal order quantities and performance measures with the EOQ model. Worksheet Learning Objective: 12-03 Evaluate optimal order quantities when there are quantity constraints or quantity discounts are offered. Difficulty: 3 HardExplanation / Answer
ANSWER
Explanation
A
EOQ
Purchase price P per unit (case), P= $105
Ordering cost, O= $300 per order
Annual Carrying cost per unit, C =0.25*$105= $26.25
Weekly demand= 50
Annual Demand, d = 52*50 = 2600 cases
Optimal order quantity, E.O.Q
= SQRT(2 × Annual demand × Cost Per Order / Carrying Cost per unit per year)
= SQRT(2*2600*(300/26.25))
=243.78
EOQ=244 units
B
Order quantity, Q = 275 units
Annual inventory costs = annual ordering + annual holding costs
=(D/Q).O + (Q/2)C
=(2600/275)*300+(275/2)*26.25
=$ 6445.74
C
Order quantity, Q = 100 units
Annual inventory costs = annual ordering + annual holding costs
=(D/Q).O + (Q/2)C
=(2600/100)*300+(100/2)*26.25
=$ 9112.5
Number of cases sold =2600
Sum of ordering +holding cost for each case sold
= $ 9112.5/2600
= $3.51
D
EOQ =244 units
Millennium is supposed to order in multiples of 50. The EOQ lies between 200 and 250.so either one that gives the least sum of annual ( holding + ordering) costs
Order quantity, Q = 200 units
Annual ordering + annual holding costs
=(D/Q).O + (Q/2)C
=(2600/200)*300+(200/2)*26.25
=$ 6525
Order quantity, Q = 250 units
Annual ordering + annual holding costs
=(D/Q).O + (Q/2)C
=(2600/250)*300+(250/2)*26.25
=$ 6401.25
So, Q=250 offers the least annual cost. Hence we should order 250 cases per order
E
5% discount if they order 1000 cases per order
Purchase price P per unit (case), P= 0.05* $105 = $ 99.75
Ordering cost, O= $300 per order
Annual Carrying cost per unit, C =0.25*$99.75= $24.94
Annual Demand, d = 2600 cases
Annual ordering + annual holding costs
=(D/Q).O + (Q/2)C
=(2600/1000)*300+(1000/2)*24.94
=$ 13250