solve the problem manually and show all calculations, formulas and explanations clearly

Button X supplies all the New Jersey Fabrics stores with eight different styles of buttons for men's dress shirts. The plastic injection molding machine can produce only one button style at a time and requires substantial time to reconfigure the machine for different buttons for the next three years, its demand can be treated as fixed and known. The relevant data for this problem appear in the table below: Assuming 8 working hours per day and 250 working days per year. Button X's accounting department has established an 18 percent annual interest rate for the cost of capital and a 3 percent annual interest rate to account for storage space. Setup costs are $20 per hour required to reconfigure the equipment for a new style. Suppose that the firm decides to use a rotation cycle policy for production of the buttons. a. What is the optimal rotation cycle time? b. How large should the lots be? c. What is the average annual cost of holding and setups at the optimal solution