Nathan Manufacturing, Inc., makes and sells specialty hubcaps for the retail automobile after-market Nathan's forecasts for its wire-wheel hubcap is 1000 units next year, with an average demand of 4 units per day (note that this plant schedules production of this hubcap only as needed, during the 250 days per year shop operates). The company is capable of producing 10 hubcaps per day. Each production run incurs a setup cost of $37.5. A hubcap can be kept in inventory through the whole year by a cost of $0.50. Unit production cost of an hubcap is $5. Currently, back-ordering is not allowed. Suppose, Nathan Manufacturing, Inc., decides to outsource the production of these hubcaps to a supplier, sa they can focus on the production of another product that will yield an annual profit of $800. The supplier also works for 250 days per year, is reliable to deliver any quantity in an exact 100 days of lead time, and does not offer any quantity discounts. The fixed cost of an order release to the supplier is $27 and the same inventory holding cost will apply ($0.50). To enable further cost reductions, Nathan will allow stock-outs this time, assuming that back-ordering one hubcap for one year will cost $2.5. Determine the maximum affordable unit purchase cost that makes the supplier's offer a reasonable choice. Also determine the reorder point that triggers the release of an order to the supplier. Carry out the whole analysis and show all of your calculations