A company is about to begin production of a new product. The manager of the department that will produce one of the components for the product wants to know how often the machine used to produce the item will be available for other work. The machine will produce the item at a rate of 200 units a day. Eighty units will be used daily in assembling the final product. Assembly will take place five days a week, 50 weeks a year. The manager estimates that it will take almost a full day to get the machine ready for a production run, at a cost of $300. Inventory holding costs will be $10 a year. a. What run quantity should be used to minimize total annual costs

Suppose general motors demands labor according to the labor demand function 푤푤= 40−0. 5퐸퐸, where 푤푤 is the hourly wage and 퐸퐸 is the number of employees. the united auto workers union has a utility function given by 푈푈=푊푊∗퐸퐸. a.in 1984, the united auto workers union started negotiations with general motors by assuming that they were a monopoly union. find the wage and employment demands that the united auto workers union would have demanded before any bargaining began. b.if general motors and the united auto workers union both had excellent bargaining representatives, would this be the final labor contract? if not, then explain in words and graphically where they would end up after the bargaining process.

6carla would like to buy a dress, a dresser for her bedroom, and a home theater system. she has one month's worth of living expenses in her emergency fund. carla decides to save for the home theater system. did carla make the right decision? why or why not? a. yes; her emergency fund is full and the other items will probably be less expensive. b. yes; she could save more for her emergency fund, but the home theater will be harder to save for. c. no; she should save more for her emergency fund because she has saved less than the recommended amount. d. no; she should have bought the dress and dresser first because she could afford them right away. reset next

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.