Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials
ID: 345006 • 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 1000 kgs of palm oil per day on average. The supplier charges a $52 delivery fee per order (which is independent of the order size) and $5 per kg. Sarah’s annual holding cost is 20%. Assume she operates and sells 5 days per week, 52 weeks per year. a. 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.) b. If Sarah orders 4250 kgs with each order, what would be the annual sum of ordering and holding costs? (Round your answer to 3 decimal places.) c. If Sarah orders 7700 kgs with each order, what would be sum of ordering and holding costs per kg sold? per kg d. Sarah’s supplier is willing to sell her palm oil at a 5% discount if she 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? Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 1000 kgs of palm oil per day on average. The supplier charges a $52 delivery fee per order (which is independent of the order size) and $5 per kg. Sarah’s annual holding cost is 20%. Assume she operates and sells 5 days per week, 52 weeks per year. a. 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.) b. If Sarah orders 4250 kgs with each order, what would be the annual sum of ordering and holding costs? (Round your answer to 3 decimal places.) c. If Sarah orders 7700 kgs with each order, what would be sum of ordering and holding costs per kg sold? per kg d. Sarah’s supplier is willing to sell her palm oil at a 5% discount if she 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
Daily demand = 1000 kg
Number of days per year = 52 x 5 days = 260 days
Annual demand (D) = 1000 kg x 260 days = 260000 kg
Ordering cost (S) = $52 per order
Holding cost (H) = 20% of cost = 20% of $5 = $1
a) Economic order quantity (Q*) = sqrt of (2DS / H)
= sqrt of [(2 x 260000 x 52)/1]
= sqrt of 27040000
= 5200 kgs
So in order to minimize the total cost Sarah should order 5200 kgs with each order.
b) If the order quantity (Q) = 4250 kg
Annual Ordering cost = (D/Q) S = (260000/4250)52 = $3181.176
Annual holding cost = (Q/2)H = (4250/2)1 = $2125
Annual sum of ordering and holding cost = $3181.176 + $2125 = $5306.176
C) If the order quantity (Q) = 7700 kgs
Annual Ordering cost = (D/Q) S = (260000/7700)52 = $1755.84
Annual holding cost = (Q/2)H = (7700/2)1 = $3850
Total annual cost = $1755.84 + $3850 = $5605.84
Total cost per kg sold = Total annual cost / D = $5605.84/260000 kg = $0.02 per kg
d) If the order quantity (Q) = 15000 kgs,
Cost per kg = $5 - 5% of $5 = $5-$0.25 = $4.75
Holding cost (H) = 20% of cost = 20% of $4.75 = $0.95
Annual Ordering cost = (D/Q) S = (260000/15000)52 = $901.33
Annual holding cost = (Q/2)H = (15000/2)0.95 = $7125
Annual sum of ordering and holding cost = $901.33 + $7125 = $8026.33
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