Math 106 Quiz 4 Spring 2017 Professor: Jose R. Martinez Castillo Name: Cory Drummond Instructions: This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. Calculators, spreadsheet software, and mortgage calculators are authorized for use. If you use spreadsheet software or mortgage calculators, you must attach copies of your spreadsheet/calculator output to get credit for your answer(s). You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. If you have any questions, please contact me by e-mail (Jose.Martinezcastillo@faculty.umuc.edu). At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. I certify that I have not used any instructor solutions manuals or online problem solving services. Name: Date: 1) A survey of 62 people gave the following results: 38 read Newsweek Magazine, 26 read Time, and 14 read both Newsweek and Time. n() = 62 Total # of people. n(NW) = 38 People who read Newsweek magazine. n(T) = 26 People who read time. n(NWT) = 14 People who read both. a. How many read neither Newsweek nor Time? 62 - 38 - 26 + 14 = 12 b. How many read Newsweek Magazine only? 38 - 14 = 24 c. How many read Time Magazine only? Math 106 Quiz 4 Page 2 26 - 14 = 12 2) In how many ways can a party of ten persons arrange themselves when sitting in a row of ten chairs A) 1010 B) 9 8 7 6 5 4 3 2 1 C) 210 D) 10! E) none of these 10P10 = 10! = 3,628,800 3,628,800 ways to arrange themselves. 3) List the elements of the sets defined by the following: a. {-5, 0, 2, 9} {- 5, -1, 3, 9, 17} ____________________________ b. {4, 6, 8 {5, 7} __ c. ({4, 6, 8} {2, 4, 6} { -6, 0} _____ ____________ _________ ______________________ 4) Maximize the objective profit function P = 2x + 5y subject to: x + y 6, x - y 2, x0 y0 Insert an image from a graphing calculator or use the grid below if desired - you must show the feasible region and identify critical (corner) points to receive full credit! Math 106 Quiz 4 Page 3 y x . Maximum profit occurs at x = _________ , y = ____________ Suppose that A = {1, 3, 5, 7, 9}, B = {1, 3, 7}, and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. List the elements of the indicated set. 5) not B 6) A not B 7) U not A Math 106 Quiz 4 Page 4 8) A hotel has 100 standard rooms and 20 suites, and is currently undergoing renovations. The standard room requires 20 man-hours of labor and $4000 of capital to update, while the suite requires 30 man-hours of labor and $10000 of capital. The hotel is not willing to spend more than 1000 man-hours of labor and $300,000 of capital. Once the renovations are complete, the hotel forecasts a monthly profit of $2000 for the updated standard room, $1000 for the nonupdated standard room, $6000 for the updated suite, and $4500 for the non-updated suite. How many of each type of room should the hotel renovate in order to maximize the monthly profit? 9) If n(A) = 60, n(B) = 90, n(A B) = 20, and n(U) = 160, complete the following table. (Go to Content > Course Resources > eReadings and select \"Week 4: Counting - Contingency Table Construction and Use\" for an explanation of what goes in this table.) A B B' Totals A' Totals Math 106 Quiz 4 Page 5 10) Six volunteers are randomly selected from a crowd. They could be all men, all women, or some of each. How many groupings are possible? Solve using the multiplication principle of counting. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. I certify that I have not used any instructor solutions manuals or online problem solving services. Name: Cory Drummond Date: 17 July 2017 End of quiz: please remember to sign and date the honor statement in the box on the first page of the quiz