Bart's Barometer Business $(BBB)$ is a retail outlet that deals exclusively with weather equipment. Currently BBB is trying to decide on an inventory and reorder policy for home barometers. These cost BBB $$50$ each and demand is about $500$ per year distributed fairly evenly throughout the year. Reordering costs are $$80$ per order and holding costs are figured at $20\%$ of the cost of the item. BBB is open $300$ days a year $(6$ days a week and closed two weeks in August$).$ Lead time is $60$ working days.

a$.$ Develop a total cost model for BBB$.(4$ point$)$

b$.$ What is the optimal reorder quantity? $(5$ points$)$

c$.$ What is the cycle time? $(5$ points$)$

d$.$ What is the reorder policy for BBB $?(5$ points$)$

e$.$ What total annual cost does the model give? $(5$ points$)$