Sarah\'s Organic Soap Company makes organic liquid soap. One of the raw material
ID: 359859 • Letter: S
Question
Sarah's Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 1200 kgs of palm oil per day on average. The supplier charges a $62 delivery fee per order (which is independent of the order size) and $5 per kg. Sarah's annual holding cost is 15%. Assume she operates and sells 5 days per week, 52 weeks per year. If Sarah wants to minimize her annual ordering and inventory holding costs, how much palm oil should she purchase with each order (in kgs)? kgs (Round to nearest integer.) h If Sarah orders 4500 kgs with each order, what would be the annual sum of b. ordering and holding costs? (Round your answer to 3 decimal places.) If Sarah orders 8500 kgs with each order, what would be sum of ordering and holding costs per kg sold? hee 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
1) Daily demand = 1200 kgs kgs
Number of days in a year = 52 weeks x 5 days = 260 days
Annual demand (D)=Daily demand x number of days in a year
= 1200 x 260 = 312000 kgs
Ordering cost (S) = $62
Cost per kg = $5
Holding cost (H) = 15% of cost = 15% of $5 = $0.75
a) Economic order quantity = sqrt of (2DS / H)
= sqrt of [(2 x 312000 x 62) / 0.75]
= 7182 kgs
So if Sara wants to minimize her annual Ordering and inventory holding cost, she should order 7182 kgs with each order
b) If order quantity (Q) = 4500 kgs
Ordering cost = (D/Q) S = (312000/4500)62 = $4298.667
Holding cost = (Q/2)H = (4500/2)0.75 = $1687.5
Annual sum of cost = Ordering cost + Holding cost
= $4298.667 + $1687.5
= $5986.167
c) If order quantity (Q) = 8500 kgs
Ordering cost = (D /Q) S = (312000/8500)62 = $2275.76
Holding cost = (Q/2)H = (8500/2)0.75 = $3187.5
Total annual cost = $2275.76+$3187.5 = $5463.26
Cost per kg sold = Total annual cost / D
= $5463.26 / 312000
= $0.02 per kg
d) If order quantity(Q) = 15000 kg
Cost per kg = $5 - (5% of $5) = $5 - $0.25 = $4.75
Holding cost(H) = 15% of cost = 15% of $4.75 = $0.71
Ordering cost = (D /Q) S = (312000/15000)62 = $1289.6
Holding cost =(Q/2) H = (15000/2)0.71 = $5325
Annual Sum of cost = Ordering cost + Holding cost
= $1289.6 + $5325
= $6614.6
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