Corn Soy Oats Fish Min Max

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1 9 diet.xls A B C D E F G Diet Problem Corn Soy Oats Fish Min Max Protein 9 0 Calcium 0 0 Fat Calories Cost/Unit Decision Variables, >= 0 Feed Provided Cost Protein =SUMPRODUCT(B:E,B$:E$) =SUMPRODUCT(B:E,B:E) Calcium =SUMPRODUCT(B:E,B$:E$) Fat =SUMPRODUCT(B:E,B$:E$) Objective, Minimize Calories =SUMPRODUCT(B:E,B$:E$) Constrained >= F:F Constrained <= G Formulas

2 bikewheel.xls 9 A B C D E F Bicycle Wheel Production Problem -- "Grid" Version Activities Make Make Make Spokes Rims Wheels Limit Machine Time Labor Spokes 0 - $ 0. Unit Rims 0 - $.00 Selling Wheels 0 0 $ 0.00 Price Direct Unit Cost $ 0.0 $.00 $.00 Amount of Activity Usage of Revenue $,00.00 Machine Time Cost $,00.00 Labor Profit $,0.00 Amount Sold Spokes.E- Rims 0 Wheels 0 Values

3 bikewheel.xls 9 A B C D E F Bicycle Wheel Pr Activities Make Make Make Spokes Rims Wheels Limit Machine Time Labor Spokes 0-0. Unit Rims 0 - Selling Wheels Price Direct Unit Cost 0.0 Amount of Decision Variables >= 0 Activity Constrained <= E:E Usage of Revenue =SUMPRODUCT(E:E,B:B) Machine Time =SUMPRODUCT(B:D,B$:D$) Cost =SUMPRODUCT(B:D,B:D) Labor =SUMPRODUCT(B:D,B$:D$) Profit =E-E Amount Sold Spokes =SUMPRODUCT(B:D,B$:D$) Objective, Maximize Rims =SUMPRODUCT(B9:D9,B$:D$) Wheels =SUMPRODUCT(B:D,B$:D$) Constrained >= 0 Formulas

4 perfume.xls 9 A B C D E F Perfume Problem -- "Grid" Version Activities Process Refine Refine Raw Material Brute Chanelle Limit Raw Material Lab Time 000 Regular Brute - 0 $.00 Unit Luxury Brute 0 0 $.00 Selling Regular Chanelle 0 - $.00 Price Luxury Chanelle 0 0 $.00 Direct Unit Cost $.00 $.00 $.00 Amount of 000..E- Activity Usage of Revenue $,. Raw Material 000 Cost $,. Lab Time 000 Profit $,. Amount Sold Regular Brute. Luxury Brute. Regular Chanelle 000 Luxury Chanelle.E- Values

5 perfume.xls 9 A B C D E F Perfume Problem Activities Process Refine Refine Raw Material Brute Chanelle Limit Raw Material Lab Time 000 Regular Brute - 0 Unit Luxury Brute 0 0 Selling Regular Chanelle 0 - Price Luxury Chanelle 0 0 Direct Unit Cost Amount of Decision Variables, >=0 Activity Constrained <= E:E Usage of Revenue =SUMPRODUCT(E:E,B:B) Raw Material =SUMPRODUCT(B:D,B$:D$) Cost =SUMPRODUCT(B:D,B:D) Lab Time =SUMPRODUCT(B:D,B$:D$) Profit =E-E Amount Sold Regular Brute =SUMPRODUCT(B:D,B$:D$) Objective, Max Luxury Brute =SUMPRODUCT(B9:D9,B$:D$) Regular Chanelle =SUMPRODUCT(B:D,B$:D$) Constrained >= 0 Luxury Chanelle =SUMPRODUCT(B:D,B$:D$) Formulas

6 9 9 0 hiring.xls A B C D E F G H I J K L M N O Hiring Students Min Shifts Availability Mon Tue Wed Thu Initials Profit/Shift AM PM AM PM AM PM AM PM AM PM Max shifts CM FI GR HS JD JE SR TR Fri Decision Variables (Binary) Assign Shift Mon Tue Wed Thu Fri Logical Bounds Initials Hire? AM PM AM PM AM PM AM PM AM PM Total Lower Upper =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M9 =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M =A =SUM(C:L) =B*B$ =B*M Filled by =SUM(C:C) =SUM(D:D) =SUM(E:E) =SUM(F:F) =SUM(G:G) =SUM(H:H) =SUM(I:I) =SUM(J:J) =SUM(K:K) =SUM(L:L) Added Profit/Week >= N:N =SUMPRODUCT(B:B,M:M) Decision <= O:O Variables (Binary) Constrained = Objective, Maximize <= C:L Formulas

7 Table.: Customer Requirement (tons) Table.: Fixed Annual Cost Plant $,000 Plant $,000 Plant $ 0,000 Plant $,000 Plant $ 0,000 Warehouse $ 0,000 Warehouse $,000 Warehouse $ 0,000

8 Values A B C D E F G H I J K Huntco Plant/Warehouse Location Problem Plant to warehouse unit production, shipping costs, plant fixed costs Warehouse Fixed cost $00 $,000 $,0 $,000 $00 $00 $00 $,000 Plant $00 $00 $00 $0,000 $00 $00 $00 $,000 $00 $00 $00 $0,000 Warehouse to customer unit shipping costs, warehouse fixed costs Customer Fixed cost $0 $0 $90 $0 $0,000 Warehouse $0 $0 $0 $0 $,000 $0 $0 $0 $0 $0,000 Plant to warehouse shipments (tons) Warehouse Logical upper bound Use plant? Capacity Shipped <= <= 0 0 Plant <= <= <= Received = = = Shipped Warehouse to customer shipments (tons) Customer Logical Use upper bound warehouse? Total demand Shipped <= Warehouse <= <= Received = = = = Required Summary of costs Plant to warehouse costs $0,000 Warehouse to customer costs $,00 Plant fixed costs $,000 Warehouse fixed costs $0,000 Total cost $00,00 HUNTCO.XLS

9 Formulas A B C D E F G H I J K Huntco Pl Plant to war Warehouse Fixed cost Plant Warehouse Customer Fixed cost Warehouse Plant to war Warehouse Decision Variables >= 0 Logical upper bound Use plant? Capacity Shipped =SUM(C:E) <= =I*J.9E =SUM(C:E) <= =I*J 0 Plant =SUM(C:E) <= =I*J =SUM(C:E) <= =I*J =SUM(C:E) <= =I*J 00 Received =SUM(C:C) =SUM(D:D) =SUM(E:E) = = = Shipped =TRANSPOSE(G:G) =TRANSPOSE(G:G) =TRANSPOSE(G:G) Decision Variables, Binary Warehouse Decision Variables >= 0 Constraints Customer Shipped Logical upper bound Use warehouse? Total demand.0e-0.9e-0.90e =SUM(C:F) <= =J*K 0 =SUM(C$9:F$9) Warehouse =SUM(C:F) <= =J*K =SUM(C$9:F$9) =SUM(C:F) <= =J*K =SUM(C$9:F$9) Received =SUM(C:C) =SUM(D:D) =SUM(E:E) =SUM(F:F) = = = = Required Constraints Summary of Plant to ware =SUMPRODUCT(C:E,C:E) Warehouse t =SUMPRODUCT(C:F,C:F) Plant fixed co =SUMPRODUCT(G:G,I:I) Warehouse f =SUMPRODUCT(H:H,J:J) Objective, Min Total cost =SUM(D:D) HUNTCO.XLS

10 Selling Calendars: Example "Newsboy Problem" Selling Newspapers: An Example Problem with Probability You run a newspaper stand. You cannot predict exactly how many copies of the Daily Blab newspaper, but in the past, you have observed the following demand pattern: Demand Percentage of the Time % % % % % % % % % 9 % 0 % % % % % % % % % 9 % 0 % Each copy of the Daily Blab costs you $0. and sells for $0.. You must place your order for the papers the night before they are sold, before you know exactly how many copies you will be able to sell. Unsold copies may be returned to the publisher at the end of the day for a credit of $0.0 each. You can buy the paper only in multiples of, and are considering stocking either,, 0,, or 0 papers per day. What is the right number of papers to order each night? [/0/0 ::9 PM]

11 newspaper.xls 9 A B C D E F G Newspaper Problem Possible Demand Probability Stock Cost per paper $ 0. % Levels Retail price $ 0. % Return credit $ 0.0 % % 0 Stock Level % % 0 Demand % % Sales % Left Over 0 9 % 0 % Revenue $ 9.00 % Cost $.00 % Return credit $ - % Profit $.00 % % % % % 9 % 0 % 0% Expected Value 9.99 Values

12 newspaper.xls 9 A B C D E F G Newspaper Problem Possible Demand Probability Stock Cost per paper Levels Retail price Return credit =G+ 0.0 =G+ Stock Level =Parameter(G:G,,A) 0.0 =G+ 0.0 =G+ Demand =gentable(d:d,e:e) Sales =MIN(B,B9) 0.0 Left Over =B-B Revenue =B*B 0.0 Cost =B*B 0.0 Return credit =B*B 0.0 Profit =simoutput(b-b+b,a) =SUM(E:E) Expected Value =SUMPRODUCT(D:D,E:E) Formulas

13 YASAI Simulation Output Workbook newspaper.xls YASAI Version:. Sheet Values Use Same Seed? Yes Start Date /0/0 Random Number Seed: Start Time :0: PM Run Time (h:mm:ss) 0:00:0 Scenarios: Sample Size: 00 Parameter Scenario Stock Level 0 0 Output Name Scenario Observations Mean Standard Deviation Profit Profit Profit Profit 00.. Profit A stocking level of gives the highest expected profit, although the expected demand level is almost exactly 0.

14 repairshop.xls A B C D E F G H Repair Shop Simulation Model Taxis in fleet 00 Breakdown probability 0.% Taxi Opportunity Cost/Day $ 0.00 Mechanics Larry Moe Curly Cost/day $ $.00 $ 0.00 Chance can fix.0%.% 0.0% 0.0%.% 0.0% 0.0%.%.0% Average..0. Hiring Scenario 0 Cost: Mechanics $,000 Cost: Taxis out of Service $,00 Total Cost $,00 Average Taxis in Shop Can Fix In Shop At Day Larry Moe Curly Start End Breakdowns (etc. to 0 days)

15 repairshop.xls A B C D E F G H Repair Shop Simulation Model Taxis in fleet 00 Breakdown probability 0.00 Taxi Opportunity Cost/Day 0 Mechanics Larry Moe Curly Cost/day 00 0 Chance can fix 0. =/ =/ =/ 0. Average =SUMPRODUCT($A:$A,B:B) =SUMPRODUCT($A:$A,C:C) =SUMPRODUCT($A:$A,D:D) Hiring Scenario =Parameter({,0},,B) =Parameter({,0},,C) =Parameter({,0},,D) Cost: Mechanics =0*SUMPRODUCT(B:D,B:D) Cost: Taxis out of Service =B*SUM(E:E) Total Cost =simoutput(sum(b:b),a) Average Taxis in Shop =simoutput(average(e:e),a) Can Fix In Shop At Day =B =C =D Start End Breakdowns =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E9-SUMPRODUCT(B9:D9,B$:D$)) =genbinomial(b$-e9,b$) =A9+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F9+G9 =MAX(0,E0-SUMPRODUCT(B0:D0,B$:D$)) =genbinomial(b$-e0,b$) =A0+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F0+G0 =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E9-SUMPRODUCT(B9:D9,B$:D$)) =genbinomial(b$-e9,b$) =A9+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F9+G9 =MAX(0,E0-SUMPRODUCT(B0:D0,B$:D$)) =genbinomial(b$-e0,b$) =A0+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F0+G0 =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) =A+ =gentable($a$:$a$,b$:b$) =gentable($a$:$a$,c$:c$) =gentable($a$:$a$,d$:d$) =F+G =MAX(0,E-SUMPRODUCT(B:D,B$:D$)) =genbinomial(b$-e,b$) (etc. to 0 days)

16 YASAI Simulation Output Workbook horses.xls YASAI Version:. Sheet Values Use Same Seed? Yes Start Date //0 Random Number Seed: Start Time Run Time (h:mm:ss) 0:0: Scenarios: Sample Size: 00 :: PM The best profit is obtained by renting the small corral only. The average number of horses left in the corral is about.. The probability of making less than $,000 is about %. Parameter Scenario Corral Capacity Corral Cost/Day $.00 $0.00 $.00 0 $0.00 Output Name Scenario Observations Mean Standard Deviation Adjusted Total Profit Adjusted Total Profit Adjusted Total Profit Adjusted Total Profit Average Left in Corral Average Left in Corral Average Left in Corral Average Left in Corral Less Than $,000? Less Than $,000? Less Than $,000? Less Than $,000? Total Profit Total Profit Total Profit Total Profit

17 Belt Replacement Example Problem Part Replacement: A Dynamic Simulation Model Your factory's production equipment contains a belt that must operate under extreme environmental conditions. The belts fail frequently, and the exact probability of failure depends on a belt's age, as follows: Day of Use Chance of Belt Failure % % % % % or more 0% If a belt fails while in use, it must be replaced on an emergency basis. This causes you to lose the remainder of the day's production on the equipment, with a cost uniformly distributed between $00 and $00. In this case, you start the next day with a fresh belt. A working belt can also be replaced just before the start of any day's production. This scheduled replacement is much cheaper than emergency replacement, costing only $0, and allows you to start that day with a fresh belt. The firm's strategy is to replace each belt after n days of use, or as soon as it fails, whichever comes first. What is the best choice of n out of the possibilities,,,,, and? Simulate each policy for 0 days with a sample size of 00. Assume that you start the 0-day period with a scheduled replacement. For the best policy, what is the average number of scheduled and emergency replacements in the 0-day period? [/0/0 :: PM]

18 Snowboard luggage x = Units of small luggage produced x = Units of medium luggage produced x = Units of large luggage produced t = Dollars spent on trade promotions d = Dollars spent on direct promotions max x + 0x + 0x [0.x + x +.x ] [x + x + x ] (t + d) ST 0.x + x +.x 0 x + x + x 9000 x = t + 0.d x = t + 0.d x = t + 0.0d x, x, x, t, d 0 (Note: x, x, x 0 are redundant and don t absolutely have to be included.) Feeding emus (a) The uncontrollable inputs (parameters) are in B:G, B:E, B:B, and F9 (b) The changing cells are B:E (c) =SUMPRODUCT(B:EB$:E$) (d) =SUMPRODUCT(B:E,B:E) + (-B)*SUMPRODUCT(B:E,B:E) (e) =SUMPRODUCT(B:E,B:E) + B*SUMPRODUCT(B:E,B:E) (f) =F9*F (g) =SUMPRODUCT(B:E,B:E) (h) =B*F (i) Target cell is E, minimize F <= B9 B:E <= B B:B >= F:F B:B <= G:G Assume linear model (Note that the formulas in B:E are nonlinear, but since they are not used in the solver model, you can still assume nonlinear. If you have the constraint B:E <= F9 instead of B:E <= B, then you cannot assume linear model.)

19 Feeding emus algebraically Again, I think this is the hardest problem in this collection. Note that there is no fruit mix. x = Pounds of raw corn fed to the emus x = Pounds of raw wheat fed to the emus x = Pounds of raw fishmeal fed to the emus y = Pounds of converted corn fed to the emus y = Pounds of converted wheat fed to the emus y = Pounds of converted fishmeal fed to the emus min (x + y ) +.(x + y ) +.(x + y ) +(y + y + y ) ST y + y + y. x + y 0.(x + y + x + y + x + y ) x + y 0.(x + y + x + y + x + y ) x + y 0.(x + y + x + y + x + y ) 00 (x + y ) + 0(x + y ) + 0(x + y ) (x + y ) + (x + y ) + 0(x + y ) 0 0 0(x + 0.y ) + 0(x + 0.y ) + (x + 0.y ) (x + y ) + 0(x + y ) + (x + y ) + 0. (0y + 0y + y ) 00 x, x, x, y, y, y 0 Photo-chemicals (a) C = B B C = C + B B (b) C = ( F$)*C + B B DigivNav x = number of standard units produced x = number of deluxe units produced max (00)(0.9)x + (0)(.9)x [ 0,000 x +,000 x 0 + (x 0 + x ) ] ST x + x 0 x + x (0)() 0.9x 0. (0.9x + 0.9x ) x, x 0

20 (e) B = SUM(B:B) C = SUM(C:C) (or just copy cell B) (f) = D*B (g) D = D*C D = SUMPRODUCT(B:B,B:B) D = D*B D = D*SUM(D:D) D = D SUM(D:D) (h) Target cell is D, maximize Changing cells are B:C B:B <= D (milk processing limit) B:B >= D0 (% minimum per month) B:B >= E:E (% decrease rule) B:B <= F:F (% increase rule) C:C >= D:D (minimum cheese sales) C:C <= E:E (maximum cheese sales) D:D >= 0 (ending inventory) Assume linear model If you examine the model, you may conclude that assume nonnegative isn t necessary because of all the other constraints that are present. However, there is no harm in including assume nonnegative. Cable TV x i = Start time (in weeks) of activity i = A, B,..., F d = Number of weeks until we declare the project done. min d x A 0 x B x A + x C x B + x D x B + x E x C + x E x D + x F x B + d x E + d x F + Note: additional constraints d x A +, d x B +, d x C +, d x D +, and x B,..., x F 0 may be included, but would be redundant for this particular problem.

21 Final Exam Practice Material Operations Management: Study Guide and Practice Questions for Final Exam (Updated December 0) This study guide is meant to give you an idea of what to expect on the final exam. There will three questions that will cover the material on linear and integer programming. These questions may arbitrarily combine the model elements listed below. One of these questions will be spreadsheet/solverbased, and the rest will be algebra-based. Linear Programming Model Elements Resource allocation/production planning, diet Process models (one process making multiple things, one operation feeding material into another, etc.) Multi-period inventory/production Transportation models Blending constraints Investment models Project scheduling, including crashing (note also the trick of minimizing the maximum of a number of things, as we did with declare done in project scheduling) (Mixed) Integer Programming Model Elements Definition of integer and binary variables Knapsack constraints Logical constraints (one of n possibilities must or may be true, etc.) Assignment models, grids of binary variables Fixed charge models, logical upper and lower bounds Set covering and partitioning There will also be two questions on probability and simulation, based on YASAI spreadsheets. These questions will draw on the following topics: Probability, Simulation, and YASAI Random variables (what are they?), and specifically Poisson Binomial (including setting the first argument to to get a 0/ result) Uniform Normal From a table (GENTABLE) How to use YASAI, including PARAMETER (including testing all combinations of several parameters) SIMOUTPUT YASAI dialog box Interpretation of output report, including percentiles Using a 0/ output to estimate the probability of an event Static models (like NEWSBOY) Dynamic models (like INVENTORY)

22 Final Exam Practice Material Using the central limit theorem to approximate a sum of lots of independent things as a single Normal random variable You should also when and when not to use absolute references ($ signs). It may also be helpful to recall how the following Excel functions work: IF INDEX SUMPRODUCT INT MIN TRANSPOSE MAX SUM SQRT Exam Rules The exam will be three hours long. The ground rules for the test are similar to midterm, except that two (double-sided) sheets of notes are permitted. You may want to use these sheets to remember the syntax of various Excel and YASAI functions. The sheets must be handwritten in your own handwriting. The only other materials allowed in the exam will be a calculator (which should not be absolutely necessary), and a dictionary, if English is not your native language. Suggested Study Plan. Review the course pack examples and your notes from class to make sure you are familiar with the basics of the material. In particular, you may be rusty on algebra formulation and the linear programming material that we covered in the first weeks of the course. In recent semesters, the majority of points lost on final exams came on material that appeared before or near the first midterm, so make sure you review that material.. Study the review questions below. They are mostly taken from prior final exams. I strongly suggest trying to do each question yourself, and then look at the answers. Studying the questions and answers simultaneously without attempting the problems yourself will not be as beneficial.. Review the practice materials for the midterms. Of particular interest may be the problems DigiNav, Simulating Semiconductor Fabrication, and Selling Dresses by Catalog Review Questions: Notes We used to divide questions for linear and integer programming into separate categories. We may now ask questions that combine topics from linear and integer programming (as in Producing Biotech Chemicals below). Some of the simulation problems were based on a different simulation which we no longer use. It is quite similar to YASAI, although the output reports have a different format. We have tried to adapt the questions to YASAI as much as possible. You should ignore the minimum and maximum columns in output reports.

23 (e) E = C D (f) F = GENBINOMIAL(G,E$) (g) G = G F + D (h) E = E*SUM(G:G) E = E*E*E E = E*SUM(F:F) E = E*SUM(E:E) E = SIMOUTPUT(E SUM(E:),D) E = SIMOUTPUT(IF(SUM(E:E)>,0,),D) (i) Best choice is pieces (scenario ) (j) Probability estimate is 9.%

ADVANCED SPREADSHEET APPLICATIONS (235)

Page 1 of 7 Contestant Number: Time: Rank: ADVANCED SPREADSHEET APPLICATIONS (235) REGIONAL 2017 Job: Family Budget TOTAL POINTS (375 points) (375 points) Failure to adhere to any of the following rules