A chemical manufacturer produces a compound at the rate of 10,000 pounds a day over 250 days each year. Annual demand for that compound is 600,000 pounds per year, and each pound sells for $3.90. There is a fixed setup cost of $1,500 for each production run, and a variable cost of $3.50 for each pound produced. The following costs are incurred:

Interest rate on the cost of capital is 22% per annum (annually).

Storage and handling costs amount to 12% of the compounds cost per annum.

Answer the following questions:

1) What is the optimal production lot for the compound (write down the model name, its parameters and formula)?

2) Compute the uptime, downtime and cycle time in days, and find the cycle fraction of uptime and the cycle fraction of downtime (include the formula).

3) What are average annual holding and setup costs for the compound (include the formula)?

4) What is the annual profit for this compound?