1. As Class Convenes l Find your team’s table, have a seat, pick up Team’s Modeling Folder l Remove Chapter 3 Redos (if any) l Place your Chapter 5 Assignment and Chapter 4 Corrections in the Team’s Folder and return, in alphanumeric order, before end of Contact Before Work

2. Agenda Contact Before Work5 min Task 1 and Report Out45 min Break10 min Task 2 and Report Out45 min Expectations5 min

3. Begin With the End in Mind u Chapter 7 of HTMI –Complexity and Simplification –Constraints –Feasible / Infeasible Solutions –Objective Function –Optimization –Representation Types –Resource Allocation

4. Resubmitted Work Products Resubmissions should consist of the following ( in the order specified ! ) : ¶ The original checklist with check marks on those items you believe you have improved or corrected. · The improvements you have made to the original work product; ONLY the improvements; NOT a complete, new work product. ¸ The original work product

5. How To Model It : Chapter 7 Structure Before Task u Please CLOSE YOUR BOOKS and PUT THEM AWAY for now; Thank you ! u Each INDIVIDUAL, read the problem statement on the next SLIDE;( 7 min) make notes on questions, anything that needs clarification, etc. ( N.B. Please limit your questions to words you don’t understand, etc.; this is not an opportunity for a discussion of the problem. ) u Clarification, if any( 3 min) u Each INDIVIDUAL, read the description of the first task on a(20 min) subsequent slide; discuss in your SUBteam and follow the directions on the slide u Reporting out by teams of (10 min) (1) the REPRESENTATION or MODEL you developed, (2) the list of questions you would like to ask, or (3) the assumptions you would like to make.

6. How To Model It : Chapter 7 Structure Before Task u Please CLOSE YOUR BOOKS and PUT THEM AWAY for now; Thank you ! u Each INDIVIDUAL, read the problem statement ( 7 min) on the next SLIDES; make notes on questions, anything that needs clarification, etc. ( N.B. Please limit your questions to words you don’t understand, etc.; this is not an opportunity for a discussion of the problem. ) u Clarification, if any( 3 min) u Each INDIVIDUAL, read the description of the first task on a(20 min) subsequent slide; discuss in your SUBteam and follow the directions on the slide u Reporting out by teams of (10 min) (1) the REPRESENTATION or MODEL you developed, (2) the list of questions you would like to ask, or (3) the assumptions you would like to make.

7. slide 7 An Economic Problem A building contractor has acquired a 10-acre site and plans to develop it as a residential area. The contractor has two basic designs for homes: a low- income home and a middle-income home. He expects to take 5 years to complete the project. Low income homes cost $30,000 to build at a density of 20 homers per acre, whereas middle-income homes cost $40,000 to build at a density of 12 homes per acre. The contractor expects to sell a maximum of 100 low-income homes and 75 middle-income homes, but the zoning regulations will allow no more than a total of 155 homes on the site.

8. slide 8 An Economic Problem The local city council has also stipulated a formula to ensure that sufficient low-income units are built; the formula requires that there shall be at least 35 more low-income units than half the number of middle-income units. The contractor employs a work force of 60 people. The architect estimates that it will take 2.0 labor-years to build a low-income home and about 2.5 labor-years to build a middle-income home. The contractor expects to sell a low-income home for $50,000 and a middle-income home for $70,000. Your job is to advise the contractor. How many of each type of home should he build? What is the best way for the contractor to spend his money and manpower?

9. How To Model It : Chapter 7 Structure Before Task u Please CLOSE YOUR BOOKS and PUT THEM AWAY for now; Thank you ! u Each INDIVIDUAL, read the problem statement on the next SLIDE;( 7 min) make notes on questions, anything that needs clarification, etc. ( N.B. Please limit your questions to words you don’t understand, etc.; this is not an opportunity for a discussion of the problem. ) u Clarification, if any( 3 min) u Each INDIVIDUAL, read the description (20 min) of the first task on a subsequent slide; discuss in your SUBteam and follow the directions on the slide u Reporting out by SUBteams of (10 min) (1) the REPRESENTATION or MODEL you developed, (2) the list of questions you would like to ask, or (3) the assumptions you would like to make.

10. slide 10 The Task (20 minutes) Your first task is to make sure you understand the problem. In your SUBteams ê Take about 20 minutes to Organize the information you have been given in a clear, unambiguous way. Define the objectives of the exercise or problem. Decide what additional information, if any, you require and make a list of questions you wish to ask and/or assumptions you would like to make. Your time is at a premium; focus on this task and try to complete it in class. ê Use an overhead transparency to document your results for presentation. ê Your representation, or response to the requests above, could be a list, a diagram, a set of equations, a flowchart, an algorithm, or whatever format (or representation type ) you choose ! ê Do NOT actually try to solve the problem at this time.

11. slide 11 Reporting Out u When your name is called: –quickly come to the overhead –present your plan (model), questions you have, or any assumptions you made

12. slide 12

13. Break Be back with your team, ready to work, in 10 minutes : remember our class Code of Cooperation !

14. Chapter 7 (continued) Structure Before Task u Please RETRIEVE and OPEN YOUR BOOKS; Thank you ! u Solving The Problem (20 min) –Each INDIVIDUAL, read pp. 54 - 55Y up TO the next task –In your SUBteams do the next task (i.e., solve the problem) u Reporting our by teams of the steps you took (5 min) to solve the problem u Each INDIVIDUAL, read pp. 56-57Y (15 min) ( N.B. only TO ‘A Mathematical Formulation); then discuss in your SUBteam and compare your approach to the approach presented in the text u Clarifying Expectations ( 10 min)

15. Chapter 7 (continued) Structure Before Task u Please RETRIEVE and OPEN YOUR BOOKS; Thank you ! u Solving The Problem (20 min) –Each INDIVIDUAL, read pp. 54 - 55Y up TO the next task –In your SUBteams do the next task (i.e., solve the problem) u Reporting Out by teams of the steps (5 min) you took to solve the problem u Each INDIVIDUAL, read pp. 56-57Y (15 min) ( N.B. only TO ‘A Mathematical Formulation); then discuss in your SUBteam and compare your approach to the approach presented in the text u Clarifying Expectations ( 10 min)

16. slide 16 Reporting Out u When your name is called: –quickly come to the overhead –present your plan (model), questions you have, or any assumptions you made

17. slide 17

18. Chapter 7 (continued) Structure Before Task u Please RETRIEVE and OPEN YOUR BOOKS; Thank you ! u Solving The Problem (20 min) –Each INDIVIDUAL, read pp. 54 - 55Y up TO the next task –In your SUBteams do the next task (i.e., solve the problem) u Reporting our by teams of the steps you took (5 min) to solve the problem u Each INDIVIDUAL, read pp. 56-57Y (15 min) ( N.B. only TO ‘A Mathematical Formulation); then discuss in your SUBteam and compare your approach to the approach presented in the text u Clarifying Expectations ( 10 min)

19. Chapter 7 (continued) Structure Before Task u Please RETRIEVE and OPEN YOUR BOOKS; Thank you ! u Solving The Problem (20 min) –Each INDIVIDUAL, read pp. 54 - 55Y up TO the next task –In your SUBteams do the next task (i.e., solve the problem) u Reporting our by teams of the steps you took (5 min) to solve the problem u Each INDIVIDUAL, read pp. 56-57Y (15 min) ( N.B. only TO ‘A Mathematical Formulation); then discuss in your SUBteam and compare your approach to the approach presented in the text u Clarifying Expectations ( 10 min)

20. Assessment Expectations for Chapter 7 Tasks That DO Need to be Completed to Meet Expectations for This Chapter ( U:\MODELING\ASSESSMT \...\I_EXPECT.DOC, \EXPECT_7.DOC, and \CHKLST7.DOC) 1Finish reading the entire chapter and make a list of heuristics found in this chapter which you found useful or believe may be useful in the future. Specifically, summarize the heuristic found on p. 119H or p. 60Y in the text (i.e., where does the solution occur; where does it NOT occur?).

21. Assessment Expectations for Chapter 7 2Construct a chart comparable to Figure 7.5H on pp. 120H using EXCEL (or any other tool of your choice that is ‘machine readable’ by the instructor which means that the file produced can be imported to one of the Microsoft Office application programs; i.e., Word, Excel, or PowerPoint ). Highlight feasible domain on the chart. –Note that this task requires you to become proficient in developing charts which are a very common and very powerful representation type. –The use of variable (or cell) names in place of ‘hard coded’ numbers is important (see p. 125H of the How to Model It text.)

22. Assessment Expectations for Chapter 7 –See the example U:\MODELING\CLASS\XLS\CHARTS.XLS file for information on developing charts in EXCEL. –The work submitted must meet the ‘best practices’ standard for the presentation of technical work which is discussed in Section J of the Engineering Core Workbook for this class. Do make an effort to comply with the recommended practices for spreadsheets found in your competency matrix (e.g. use variable names for values rather than ‘hard coded’ numbers; see pp. 125H in the text).

23. Assessment Expectations for Chapter 7 3Show the unit consistency for each equation in your model (see example below) and display an appropriate number of significant figures in your printed output. F [lb/hr] X (1 hr/60 min) = F/60 [lb/min]

24. Assessment Expectations for Chapter 7 u Submit answers to the questions below. The answers must meet the expectations established in the ‘Assessment Expectations’ document. l What should the contractor do (justify your answer based on the results of your modeling)? l Show or describe how equations 7.5Y, 7.6Y and 7.7Y pp. 58Y were derived (i.e., explain them to yourself and summarize your explanation in your documentation). l Use your EXCEL model to answer ONE of the ‘What If’ questions on pp. 61Y (N.B. if your model has been developed using the recommended best practices, this task should not require a great deal of effort or time.).

25. slide 25 Process Check - Plus Delta u On WebNotes write one thing in today’s class that helped you learn the material u On WebNotes describe how we could improve your learning of this material