#11 value: 1.50 points PA 12-2 Sarah\'s Organic Soap Company makes organic... Sa
ID: 360681 • Letter: #
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#11
value: 1.50 points PA 12-2 Sarah's Organic Soap Company makes organic... Sarah's Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 1500 kgs of palm oil per day on average. The supplier charges a $53 delivery fee per order (which is independent of the order size) and $4.5 per kg. Sarah's annual holding cost is 20%. Assume she operates and sells 5 days per week, 52 weeks per year. aIf Sarah wants to minimize her annual ordering and inventory holding cost, how much palm oil should she purchase with each order (in kgs)? (Round to nearest integer.) h If Sarah orders 3500 kgs with each order, what would be the annual sum of ordering and holding costs? (Round your answer to 3 decimal places.) If Sarah orders 7800 kgs with each order, what would be sum of ordering and holding costs per kg sold? C. per kg Sarah's supplier is willing to sell her palm oil at a 5% discount if she d. purchases 15,000 kgs at a time. If she were to purchase 15,000 kgs per order what would be her annual sum of ordering and holding costs?Explanation / Answer
a. To minimize the ordering cost and holding cost , Sarah should order optimal quantity which is given by
Q* = SQRT ( 2* D *S/H)
where Q* - Optimal Order Quantity
D= Annual Demand -= 1500 kgs * 5 days * 52 weeks = 1500 Kgs * 260 = 390000 Kgs
S = Ordering Cost =$53
H =Holding Cost / unit = 20% of Price = 0.2 * $4.5 = $0.9
Therefore , Q* = SQRT ( 2 * 390000 * 53/0.9)
Q* = 6777 Kgs
B. If Sarah orders 3500 Kgs
Total Cost = Holding Cost + Ordering Cost = (Q* *H/2) + (D * S/Q*) = (3500 * 0.9/2) + (390000 * 53/3500)
Total Cost = $7480
C. If Sarah orders 7800 Kgs
Total Cost = Holding Cost + Ordering Cost = (Q* *H/2) + (D * S/Q*) = ( 7800 * 0.9/2) + (390000*53/7800)
Total Cost = $6160 for 390000 Kgs
Total cost per unit sold = $6160/390000 = $0.015/Kg
D. If Sarah orders 15000 Kgs with 5% discounts
Total Cost = Holding Cost + Ordering Cost = (Q* *H/2) + (D * S/Q*) = (15000 * 0.2 * 4.5 * 0.95/2) + (390000 * 53/15000)
Total Cost = $7790
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