Please include all the calculations and steps

1. HAL Ltd. produces a line of high-capacity disk drives for mainframe computers. The housings for the drives are produced in Hamilton, Ontario, and shipped to the main plant in Toronto. HAL uses the drive housings at a fairly steady rate of 720 per year. HAL Ltd. can produce the disk drive housings in the Hamilton, Ontario, plant at a rate of 150 housings per month. The housings cost HAL $85 each to produce, and the setup cost for beginning a production run is $700. Assume an annual interest rate of 28 percent for determining the holding cost.

a. Find the time between initiation of production runs, the time devoted to production, and the downtime each production cycle.

b. What is the optimal number of housings for HAL to produce in each production run?

c. What is the maximum dollar investment in housing that HAL has at any point in time?