A toy manufacturing uses 48000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can can produce at a rate of 800 per day. The toy trucks are assembled uniformly ( at a constant rate ) over the entire year. Carrying cost is $ 1 per wheel per year. setup cost for the production run of the wheel is $ 45. The firm operatyes 240 days per year. Determine each of the following:

a) Optimal manufacturing run size.

b) Resulting total annual cost for carrying inventory and for production setups.

c) Cycle time for the optimal run size.

d) Percentage of the time the wheels manufacturing line is in production mode.