Problem: Batching 

Sarah's Organic Soap Company makes four kinds of organic liquid soap- "regular", "lavender", "citrus" and "tea tree".  Demand for the four scents is 150, 120, 75 and 55 kgs per hour respectively.  Sarah's production process can produce any soap at the rate of 450 kgs per hour but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn't produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held.

a) How many kgs of "regular" should Sarah produce before switching over to another scent?

b) 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. If Sarah wants to minimize inventory holding and ordering costs, how much Palm oil should she purchase with each order (in kgs)?

c) Sarah's supplier is willing to sell 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?