A local salad dressing company, Three Rivers Dressings, produces four types of salad dressings: "Blue Cheese", "Ranch", "Italian", and "Thousand Island". Demands for the four types are 120, 90, 70, and 20 kg per hour, respectively. The company has one machine that can produce any dressing at a rate of 400 kg per hour. However, 2 hours are needed to clean the machine before switching from one dressing type to another. During the cleanup time, the machine cannot produce any product. The company needs a production schedule that (i) rotates through the four types once in one cycle, (ii) meets the required demand and (iii) minimizes the amount of inventory held. (Here it is assumed that the production machine runs 24 hours a day, 7 days a week. The goal is to satisfy supply and demand in one cycle.)

a) How many hours in a cycle is the machine engaged producing dressings?

b) How many cycles can the company run in one week?

c) Suppose each time the machine is cleaned, the company incurs a $50 cost for detergent, lubricants, and skilled labor. What is the annual cost for machine cleaning (Suppose there are 52 weeks in one year)?

d) What is the maximum inventory level in kilograms for "Blue cheese"?