Sarah needs to purchase organic Palm oil to make her soaps. She needs 1,000 kgs 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's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week.
(a) If Sarah wants to minimize inventory holding and ordering costs, how much Palm oil should she purchase with each order (in kgs)?
(b) Sarah's supplier is willing to sell her Palm oil at a 5% discount if she purchases 10,000 kgs at a time. If she were to purchase 10,000 kgs per order what would be her average inventory holding and delivery fees per day (in $s)? (Note, do NOT include her purchasing costs per day, which would be 1000 x 4.75 x 95%.)