Sarah’s Organic Soap Company makes four kinds of organic liquid soap: “regular,” “lavender,” “citrus,” and “tea tree.” Demands 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, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn’t produce any soap. Sarah’s wants to choose a production schedule that 

(i) cycles repeatedly through the four scents, 

(ii) meets the required demand, 

(iii) minimizes the amount of inventory held. 

a. Suppose Sarah’s produces 12,000 kgs of regular, 9600 kgs of lavender, 6000 kgs of citrus, and 4000 kgs of tea tree per batch. How much soap (kgs) can Sarah’s produce per hour? 

b. Suppose Sarah’s produces 12,000 kgs of regular, 9600 kgs of lavender, 6000 kgs of citrus, and 4000 kgs of tea tree per batch. What is the utilization (%) of the process? 

c. Suppose Sarah’s produces 12,000 kgs of regular, 9600 kgs of lavender, 6000 kgs of citrus, and 4000 kgs of tea tree per batch. How much inventory (kgs) do they have on average of lavender soap? 

d. How many kgs of “regular” should Sarah’s produce before switching over to another scent?