PA 122 Sarahs Organic Soap Company makes organic Sarahs Orga

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 $56 delivery fee per order (which is independent of the order size) and $4.5 per kg. Sarah\'s annual holding cost is 25%. 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)? (Round to nearest integer.) 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.) holding costs per kg sold? Sarah\'s supplier is willing to sell her palm oil at a 5% discount if she what would be her annual sum of ordering and holding costs? If Sarah orders 8200 kgs with each order, what would be sum of ordering and per kg d. purchases 15,000 kgs at a time. If she were to purchase 15,000 kgs per order

Solution

Average daily demand (d) = 1500 kg

Number of days in a year = 5 days x 52 weeks = 260 days

Annual demand (D) = D x number of days per year = 1500 x 260 = 390000 kgs

Ordering cost (S) = $56

Cost per kg = $4.5

Holding cost (H) = 25% of cost = 25% of $4.5 = $1.13

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

= sqrt [(2 x 390000 x 56) / 1.13]

= 6217.30 or rounded to 6217 kgs

So in order to minimize the annual Ordering and holding cost she should purchase 6217 kgs per order

b) If order quantity (Q) = 3500 kg

Annual Ordering cost = (D /Q) S = (390000/3500)56 = $6240

Annual holding cost = (Q/2)H = (3500/2)1.13 = $1977.5

Total cost = Ordering cost + Holding cost

= $6240 + $1977.5

= $8217.5

C) If order quantity (Q) = 8200 kgs

Annual Ordering cost = (D /Q) S = (390000/8200)56 = $2663.41

Annual holding cost = (Q/2)H = (390000/2)1.13 = $220350

Total annual cost = Ordering cost + Holding cost

= $2663.41 + $220350

= $223013.41

Total cost per kg = Total annual cost / D

= $223013.41/390000 kg

= $0.57 per kg

d) If the order quantity (Q) = 15000 kg

Cost per kg = $4.5 - (5% of $4.5) = $4.5 - $0.23 = $4.27

Holding cost (H) = 25% of cost = 25% of $4.27 = $1.07

Annual Ordering cost = (D/Q) S = (390000/15000)56 = $1456

Annual holding cost = (Q/2)H = (15000/2)1.07 = $8025

Total annual cost = Ordering cost + Holding cost

= $1456 + $8025

= $9481