Question

Sarah’s Organic Soap Company makes organic liquid soap. One of the raw materials for her soaps is organic palm oil. She needs 700 kgs of palm oil per day on average. The supplier charges a $70 delivery fee per order (which is independent of the order size) and $5.75 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 3500 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 8000 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?

Answer 1

Daily demand = 700 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

= 700 x 260 = 182000 kgs

Ordering cost (S) = $70

Cost per kg = $5.75

Holding cost (H) = 20% of cost = 20% of $5.75 = $1.15

a) Economic order quantity = sqrt of (2DS / H)

= sqrt of [(2 x 182000 x 70) / 1.15]

= 4707 kgs

So if Sara wants to minimize her annual Ordering and inventory holding cost, she should order 4707 kgs with each order

b) If order quantity (Q) = 3500 kgs

Ordering cost = (D/Q) S = (182000/3500)*70 = $3640

Holding cost = (Q/2)H = (3500/2)1.15 = $2012.5

Annual sum of cost = Ordering cost + Holding cost

= $3640 + $2012.5

= $5652.5

c) If order quantity (Q) = 8000 kgs

Ordering cost = (D/Q) S = (182000/8000)*70 = $1592.5

Holding cost = (Q/2)H = (8000/2)1.15 = $4600

Annual sum of cost = Ordering cost + Holding cost

= $1592.5 + $4600

= $6192.5

Cost per kg sold = Total annual cost / D

= $6192.5 / 182000

= $0.034 per kg