United aluminum company of cincinnati produces three grades (high, medium, and low) of aluminum at two mills. each mill has a different production capacity (in tons per day) for each grade, as follows: the company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5 tons of low-grade aluminum. it costs united 2 $6,000 per day to operate mill 1 and $7,000 per day to operate mill 2. the company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost. formulate a linear programming model for this problem.

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.

You are the manager of the packaging department in a cookie factory. (obviously, the packaging employees cannot eat the cookies that are transferred in during the period.) after your employees insert cookies into colorful packages (step 1) for display on store shelves, the packages of cookies are then boxed using cardboard cartons (step 2) for shipment to stores. each unit of product is represented by a carton of packaged cookies. the packaging department began the period with 1,000 units of cookies. during the period, 5,000 units of cookies were transferred in from the baking department and 5,500 units of cookies were transferred out to the finished goods department. the number of units of cookies in the ending inventory of the packaging department equals:

Working with a word processor requires more than just a knowledge of typing. a good word processor includes a number of tools designed to aid in formatting documents to meet the needs of the reader. in this project you will use your word-processing skills and a basic knowledge of apa style to format a research paper. the skills you will need for this project include the following: adjusting line spacing (double-spacing) breaking text into pages (page break) centering text changing the font, style, and size of the text editing text inserting page numbers inserting a table using spell check