EShack sells a model of Creative Labs blue-tooth adapter for $35 and expect to sell it for foreseeable future. Given their clout with the manufacturer, they are able to procure it at a price of $7.50. EShack estimates its daily demand to be normally distributed with mean 200 and standard deviation of 28 units. It reviews the inventory of the blue-tooth adapter once every day and places an order with the supplier using e-procurement software. The supplier lead-time for replenishment is 10 days including all manufacturing, transportation etc.

a) If EShack decides on an order up-to level of 2150 units, what is its expected on-hand inventory of Creative Labs blue-tooth adapter?

b)If EShack decides to provide 99% in-stock probability, what would the order up-to inventory level for the blue-tooth adapter be?

c) Assume that it costs EShack $0.55 per day to keep a blue-tooth adapter in inventory, while a backorder is estimated to cost 10% of the gross margin that EShack earns for each sale of Creative Labs blue-tooth adapter. What order-up-to level should Eshack choose for this blue-tooth adapter if their goal is to minimize holding and backorder costs?

PLEASE SHOW MATH