Sarah's Organic Soap Company makes four kinds of organic liquid soap - regular, lavender, citrus, and tea tree. Demand for the four scents are 150, 120, 75 and 50 kgs per hour, respectively. Sarah's production process can produce any soap at the rate of 450 kgs per hour (i.e., processing time of 1 kg of soap is 1/450[kg/hour] = 0.002222 [hour/kg]) but 1.5 hours are needed to switch between scents. During those switchover times, the process does not 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.
Q1) How many kgs of "regular" should Sarah produce before switching over to another scent?
Q2) Sarah needs to purchase organic Palm oil to make her soaps. She needs 1,000 kgs of Palm oil per day on average. The cost of palm oil the supplier charges is $4.75 per kg. The supplier charges a $60 delivery fee per order (which is independent of the order size). 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)?
Q3) Again, assume that Sarah needs 1,000 kgs of Palm oil per day. 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 the total daily cost (in $) that includes the daily inventory holding cost, daily ordering cost, and daily purchasing cost?