Sarah's Organic Soap company makes organic liquid soap. One of the raw materials for her soaps is prganic pal, oil. She needs 1,000kg of palm oil per day on average. The supplier charges a $60 delivery fee per order ( which is independent of the order size) and $4.75 per kg. Sarah annual holding cost is 25%. 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)?

b) if Sarah order 4,000 kgs with each order, what would be the annual sum of the ordering and holding costs?

c) If Sarah order 8,000 kgs with each order what would be the sum of odering and holding costs per kg sold? (Round to 3 decimal places)

d) Sarah's supplier is willing to sell her palm oil at a 5% discount if she purchases 15,000 kg at a time. If she were to purchase 15,000 kgs per oder what would be her annual sum of ordering and holding costs?