An elevator rail is assumed to meet specifications if its diameter is between 0.98 and 1.01 inches. Each year a company produces 100, 000 elevator rails. For a cost of $10/σ2 per year the company can rent a machine that produces elevator rails whose diameters have a standard deviation of σ. (The idea is that the company must pay more for a smaller variance.) Each such machine will produce rails having a mean diameter of one inch. Any rail that does not meet specifications must be reworked at a cost of $12. Assume that the diameter of an elevator rail follows a normal distribution. Round your answers to three decimal places, if necessary.

a. What standard deviation (within 0.001 inch) minimizes the annual cost of producing elevator rails? You do not need to try standard deviations in excess of 0.02 inch.

b. For your answer in part a, one elevator rail in 1000 will be at least how many inches in diameter?

In a chapter 7 bankruptcy, a debtor:

Laval produces lamps and home lighting fixtures. its most popular product is a brushed aluminum desk lamp. this lamp is made from components shaped in the fabricating department and assembled in the assembly department. information related to the 22,000 desk lamps produced annually follows. direct materials $280,000direct labor fabricating department (8,000 dlh × $24 per dlh) $192,000assembly department (16,600 dlh × $26 per dlh) $431,600machine hours fabricating department $15,200mhassembly department $20,850mhexpected overhead cost and related data for the two production departments follow. fabricating assemblydirect labor hours 150,000dlh 295,000dlhmachine hours 161,000mh 128,000mhoverhead cost $400,000 430,000required1. determine the plantwide overhead rate for laval using direct labor hours as a base.2. determine the total manufacturing cost per unit for the aluminum desk lamp using the plantwide overhead rate.3. compute departmental overhead rates based on machine hours in the fabricating department and direct labor hours in the assembly department.4. use departmental overhead rates from requirement 3 to determine the total manufacturing cost per unit for the aluminum desk lamps.

In the fall of 2008, aig, the largest insurance company in the world at the time, was at risk of defaulting due to the severity of the global financial crisis. as a result, the u. s. government stepped in to support aig with large capital injections and an ownership stake. how would this affect, if at all, the yield and risk premium on aig corporate debt?