Question

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 $6 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, а. kgs 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 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? 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?

Answer 1

Daily demand d = 1500 kg

Annual demand D = 1500*5*52 = 390000

Ordering cost S = $56

Cost = $6 per kg

Holding cost = 15% = 0.15*4 = 0.9

a)

Optimal order quantity Q

$Q=\sqrt{\frac{2DS}{H}}$

$Q=\sqrt{\frac{2*390000*56}{0.9}}$

Q = 6967 kg

b)

Order quantity Q = 3500 kg

Total Cost = Holding Cost + Ordering Cost = (Q/2)H + (D/Q)S

Total cost = (3500/2)*0.9 + (390000/3500)*56 = 7815

c)

Order quantity Q = 8500 kg

Total Cost = Holding Cost + Ordering Cost = (Q/2)H + (D/Q)S

Total cost = (8500/2)*0.9 + (390000/8500)*56 = 6394.41

Total cost per unit sold = 6396.41/390000 = 0.016 per Kg

d)

If Q = 15000 kg

Cost = (1-0.05)*6 = 5.7

Holding cost H = 0.25*5.7 = 1.425

Total Cost = Holding Cost + Ordering Cost = (Q/2)H + (D/Q)S

Total cost = (15000/2)*1.425 + (390000/15000)56 = 12143.5