# PA 12-1 (Algo) Millennium Liquors is a wholesaler… Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 45 cases. Millennium purchases each case for \$130, there is a \$300 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 15 percent. (Do not round intermediate calculations. Round your answer to the nearest whole number.) If Millennium is restricted to ordering in multiples of 50 cases (e.g., 50, 100, d. 150, etc.), how many cases should it order to minimize its annual ordering and holding costs? cases (Do not round intermediate calculations. Round your answer to 2 decimal places.) Millennium is offered a 5.00 percent discount if it purchases at least 1,000 e. cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?

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Annual demand, D = 45*52 = 2340
Unit carrying cost, h = 15% of 130 = \$20 per annum
Fixed ordering cost, K = \$300 per order.

Optimal order quantity, Q* = (2.D.K / h)^0.5

= (2*2340*300/20) ^ 0.5

= 265 units.

(d)

The optimal order quantity was 265. Multiple of 50, closest to this figure is 250 and 300. Check the total cost for these two figures.

For Q=250,

Total cost = (2340/250)*300 + (250/2)*20

= 2808 + 2500

= 5308
For Q=300,

Total cost = (2340/300)*300 + (300/2)*20

= 2340 + 3000

= 5340

So, Q= 250 is the best choice.

(e)

Unit carrying cost, h = 135 – (5/135*135)

= 135 – 5

= \$130 / case

H = 15 /135 *130

H = \$14.44

Q = 1000

Total cost = (2340/1000)*300 + (1000/2)*14.44

= 702 + 7220

Total Cost = \$7922.