Management Science MGMT 30600
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Date Created: 09/19/15
Final Exam Review Handout MGMT 306 Spring 2009 Reminders I Final Exam Wednesday May 6th from 100 PM 300 PM Sections 1 2 and 3 will have their exam in CL50 224 Sections 4 and 6 should go to WTHR 200 The seating assignment will be announced very soon You may bring 3 sheets of quotcribquot notes doublesided Stande normal distribution table will be provided if needed Bring your student ID because we will check your ID during the nal exam Topics included in the Final Exam are Conceptual Understanding of LP LP Sensitivity Analysis and Excel Solver Output Interpretation LP Formulation IP Formulation Nonlinear Programming Simulation modeling using Risk Project Management Decision Analysis including PrecisionTree Multi criteria Decision Modelling and Solution I The Graphical Solution method will not be on the exam 509 gtIQM WNH Question 1 A textile manufacturer produces two types of cotton cloth corduroy and denim Corduroy is a heavier grade of cotton cloth and as such requires 75 pounds of raw cotton to produce one yard whereas denim requires 5 pounds of raw cotton per yard A yard of corduroy requires 32 hours of processing time and a yard of denim requires 3 hours Although the demand for denim is practically unlimited the maximum demand for corduroy is 510 yards per month The textile manufacturer has a maximum of 6500 pounds of cotton available each month due to limited storage capacity and 3000 hours of processing time available each month The processing time each month is a sunk cost The cost of cotton is 10 cents per pound and it is considered a variable cost accounting for only the amount of cotton used The manufacturer sells the cloth for 385 per yard for corduroy and 275 per yard for denim The manufacturer wants to know how many yards of each type of cloth to produce each month to maximize pro t a Clearly define the decision variables you would use to solve this problem b Formulate a linear program for the above problem using only the variables defined in a c Due to a new process each type of cloth must undergo after being manufactured at most 40 of the total production can be corduroy Make the necessary changes in the original formulation to represent this restriction Define any additional variables if you need them d An agreement has been reached with the cotton supplier that enables the textile manufacturer to use more than 6500 pounds of cotton in a month According to the agreement cotton in excess of 6500 pounds can be stored in the supplier s depot during the month The supplier will charge 5 cents per pound for storage for the month and will store up to 4000 pounds each month Make the necessary changes in the original formulation to represent this situation Define any additional variables if you need them Question 2 The Tots Toys Company is trying to schedule production of two very popular toys for the next three months a rocking horse and a scooter Information about both toys is given below Beginning Required Required Production Inventory Inventory on Plastic Time Cost Cost Toy June 1st Per Toy Per Toy Per Toy Per Toy Rocking Horse 25 5 2 12 l Scooter 5 5 4 3 14 12 Plastic Time Monthly Demand Monthly Demand Summer Schedule Available Available Horse Scooter June 3500 2100 220 450 July 5000 3000 350 700 August 4800 2500 600 520 Develop a model that would tell the company how many of each toy to produce during each month You are to minimize total cost Inventory cost will be levied on any items in inventory on June 30 July 31 or August 31 after demand for the month has been satis ed The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for Sept 1 Don39t forget to de ne your decision variables Question 3 Noname B School is trying to decide how many of each type of computer to buy for its computer labs The Appease A model can only be used for spreadsheets and word processing and costs 1400 The Basic B model can be used for spreadsheets word processing and databases and costs 2000 The Capture C model can only be used for multimedia and costs 2500 Finally the Doitall D model can do any task and costs 3500 Due to class enrollments the school must have at least 100 machines capable of doing spreadsheets and word processing at least 50 machines capable of doing databases and at least 30 machines capable of doing multimedia The dealer the school is buying from has only 45 of model A available The school Wishes to minimize their total purchase cost The following is an LP formulation for the problem with solution and sensitivity analysis Let Anumber of Appease model purchased Let Bnumber of Basic model purchased Let Cnumber of Capture model purchased Let Dnumber of Doitall model purchased Minimize 1400A2000B2500C3500D Subject to A B D 2 100 constraint for spreadsheetswp B D 2 50 constraint for database course C D 2 30 constraint for multimedia course A S 45 number of model A s available A B C 2 0 Answer Report Target Cell Min Cell Name Original Value Final Value G3 Obj Min 0 218000 Sensitivity Report Ad39ustable Cells Final Reduced Objective Allowable Allowable Constraints Final Shadow Constraint Allowable Allowable a Ifenrollment in the database course is limited to 45 students instead of the original 50 what would be the new total purchase costs for all the computers b If the dealer could supply three additional model A s what would be the new total purchase costs for all the computers c If the dealer agrees to lower the price for Model C computers at what new lower price would the B school consider buying any Model C computers d The dealer has wamed that the price of Model D computers may actually increase before the purchase order goes through At what higher price would the school consider changing the order e A local community college would like to offer a 60 person multimedia course in the B school s labs so the school will need 60 instead of30 multimedia computers The community college is willing to make a onetime payment of 30000 to do this Assuming the B school gets no other advantages than this one time payment should the school take the offer Why or why not Question 4 A product manager for a soap manufacturer must decide whether or not to offer a new biodegradable laundry detergent The projected pro t from a successful detergent is 2 million whereas failure of the product would result in a loss of 1 million The manager currently thinks there is a 40 chance that the product will be successful Not offering the product would not change profits a Construct a decision tree for this decision 0 What is the optimal strategy I What is the EMV of this strategy I What is the risk profile I What is the EVPI The manager also has the opportunity to test the product before taking it to market At a cost of 100000 the product can be tested Consumer testing can be favorable a 50 chance or unfavorable Given a favorable test result the chance of product success is judged to be 80 However for an unfavorable test result the chance of product success is judged to be only 30 b Construct a decision tree in PrecisionTree for this problem I What is the optimal strategy and its expected value I What is the risk profile for this strategy Question 5 Remington Manufacturing is planning its next production cycle The company can produce three products each of which must undergo machining grinding and assembly operations The following table summarizes the hours of machining grinding and assembly required by each unit of each product and the total hours of capacity available for each operation The per unit profit from each of the products and the setup costs are listed in the table below I Product 1 I Product 2 I Product 3 I I Profit per unit I 48 I 55 I 50 I Setup cost I 1000 800 900 Since there is a heavy demand for the products the marketing department believes that all the products produced within the available capacities can be sold The management of Remington wants to determine the most profitable miX of products to produce Formulate an integerprogramming model on behalf of Remington Define any variables you use and clearly specify the objective function and constraints Question 6 Building a backyard swimming pool consists of siX major activities According to the knowledge of activities and their immediate predecessors the project network is drawn below FINISH Assume that the activity time estimates in days for the swimming pool construction project are Activity Optimistic MOSt Pmbable Pessimistic Expected Time Variance A hidden Hidden hidden 5 05 B hidden hidden hidden 4 06 C hidden hidden hidden 6 0 l D hidden hidden hidden 9 03 E l 2 3 F hidden hidden hidden 8 02 a What are the expected time and variance for activity E ll them into the above table b What are the critical activities c What is the expected time to complete the project d What is the probability that the project can be completed in 21 or fewer days Question 7 Office Automation Inc has developed a proposal for introducing a new computerized office system that will improve word processing and interoffice communications for a particular company Contained in the proposal is a list of activities that must be accomplished to complete the new office system project The following information about the activities is given Immediate Time weeks Cost 11000s1 Activig Description Predecessor Normal Crash Normal Crash A Plan needs 10 8 30 70 B Order equipment A 8 120 150 C Install equipment B 10 7 100 160 D Set up training lab A 7 6 40 50 E Conduct training lab D 10 8 50 75 F Test system C E 3 3 60 The length of the critical path for the above project is 31 weeks However the company wants to complete the project in 26 weeks Formulate a linear programming model that could be used in making the crashing decisions Multiple Choice Questions 1 Which of the following statements is correct U39 0quot 9 Sensitivity analysis of a linear program investigates how the optimal solution changes when the value of a decision variable changes b When the objective function coefficient of a variable changes the current optimal solution may become infeasible c If a constraint is not binding at the current optimal solution then its shadow price is zero d As long as the objective function coefficient of a variable is in its optimality range the optimal objective function value remains the same The earliest start time for an activity is a Based on the length of the critical path b Determined by the maximum of the earliest finish times of its immediate predecessors c The same as the latest start time of its immediate predecessor d None of the above The project management strategy of injecting additional resources in order to reduce the length of the project is called a Rushing b Panicking c Crashing d None of the above Which of the following are ways of crashing an activity a Using overtime b Hiring more workers c Using specialized equipment d All of the above Which of the following is not part of PERT a Uncertain activity durations b A list of activities and precedence relations c Activities overlapping with their immediate predecessors d A calculation of expected project completion time Which of the following statements related to decision trees are correct I The branches emanating from each decision node represent the precedence relationships between decision alternatives II The sum of probabilities of each state of nature outcome branch emanating from a given event node must be equal to one III Nodes of a decision tree can be ordered arbitrarily a OnlyI b Only II c I and II d I II and III Consider the following for Questions 7 11 The Big Ten Company BTC is considering expanding production to meet increases in demand BTC has three alternatives and the payoffs for each alternative under various market situations are presented in the table below 7 If BTC takes a conservative approach the choice will be a alternative 1 andor 2 b alternative 1 c alternative 2 d alternative 3 8 Which one of the following is correct a The regret for alternative 3 under state A is 100 b The regret for alternative 3 under state B is 40 c The maximum regret for alternative 3 is 140 d The maximum regret for alternative 3 is 80 9 Under Minimax regret approach BTC should select alternative 1 alternative 2 alternative 3 alternative 2 andor alternative 3 99 lt79 For questions 10 and 11 refer to the above payoff matrix and suppose the probabilities for the three market situations A B and C are 03 05 and 02 respectively 10 To maximize the expected pro t BTC should select alternative 1 alternative 2 alternative 3 alternative 2 andor alternative 3 99 lt79 11 Suppose BTC could hire a consultant who could predict the future with 100 accuracy Which one of the following is correct a With such perfect information BTC s expected payoff would be 130 b BTC would be willing to pay at most 44 to the consultant c The value of the perfect information provided by the consultant is 36 d The information provided by the consultant will not increase BTC s expected pro t 12 Which one of the following is correct about goal programing models a In a goalprogramming model with preemptive priorities we always permit tradeoffs between higher and lower level goals b There can only be one goal at each priority level c Deviation variables represent the difference between the target value for the goal and the level achieved d The priority levels of the goals are represented in the goal equations 13 The Royal Seas Company wants to run TV ads promoting its Caribbean cruises to highincome men highincome women and retirees The company is considering four ad campaigns namely A B C D and would like to select a campaign with the objectives of minimizing the cost of the campaign and maximizing estimated exposures to the target audience exposures The Royal Seas Company can eliminate from consideration campaigns a A and B b B and C c C and D d A and D Consider the following for Questions 14 15 and 16 The Lo on Company a distributor of exercise equipment wants to decide on how many units to order from two of the most popular models The company has developed the following linear program to maximize its pro ts but found out that it is infeasible x Number of units to be ordered from model 1 y Number of units to be ordered from model 2 Max 5x 3y st Storage constraint 2x y s 10 Budget constraint 2x 3y g 24 Demand constraint x y 2 16 x y 2 0 In revision Lo on drops the original objective and establishes the following three goals in order of importance Priority 1 Goal 1 Don t exceed 10 in the storage constraint Priority 2 Goal 2 Don t exceed 24 in the budget constraint Priority 3 Goal 3 Don t fall short of 16 in the demand constraint Let dr be the overachievement of goal i and let di39 be the underachievement of goal i 14 Converting the inequality 2x y S 10 into a goal equation will result in the following a 2xyd1d139 10 b 2xyd139d1 10 c 2xyd139d1 10 d 2xyd1d139 10 15 Which one of the following is the goal equation for goal 3 a xyd3d33916 b xyd339d3 16 c x y d 16 d x y d339 l6 16 What will be the new objective function 3 M11 13101134r P2 12 P3 13 b Max P1d1 P2 12Jr P3 13 0 NEH P1 11 P2 12 P3 13 d M11 P1 11 131 12 P2 13 Solutions to Review Problems for the Final Exam of MGMT 306 l a C of yards of corduroy produced each month D of yards of denim produced each month Pro t per yard of corduroy 385 7 75 10 310 Pro t per yard of denim 275 7 5 10 225 b Max 3100 225D st 75C 5D S 6500 32C 3D S 3000 CS510 CDZ 0 c C S4CDor6C4DSO d Let E of pounds of cotton used in excess of 6500 lbs Max 310C 225D 7 005E st 75C 5D S 6500 E 32C 3D S 3000 C S 510 E S4000 C D E 2 0 Pg number of toy i to produce in month j Sij surplus inventory of toy i at end of month j 12P1112P12 12P13 14P2114P22 14P23 1su1s12 1S13 12321 12322 12323 P11 S11 195 811 P12 S12 350 S12 P13 S13 600 13 3 150 P21 S21 S21 P22 S22 700 S22 P23 S23 520 S23 260 5P11 41321 3500 5P12 4Pzz 5000 5P13 4P23 f 4800 2P11 3P21 2100 2P12 3Pzz 3000 2P13 3P23 2500 Pg Sij 2 0 3 a It would not change since the SP 0 and allowable decrease is in nity b It would reduce by 6003 1800 since SP 600 and 3 units is within allowable increase New value will be 218000 7 1800 216200 c Reduced cost 1000 Ifthe cost goes down to 2500 7 1000 1500 or less we would consider buying Model C d Allowable increase is 1000 If it increases to over 3500 1000 4500 we would change the order e Allowable increase 25 With an increase to 55 from 30 our cost will increase by 25 1500 37500 When we increase RHS by 30 the cost may increase even more A payment of 30000 would not cover our costs We should reject 4 See attached excel le for solution 5 Decision variables x1 number of units of each product produced I if producti is produced yz 0 otherwise max 48x1 55x2 50x3 71000y1 800y2 900y3 st 2x13x2 6x3 S 600 6x13x2 4x3 S 300 5x1 6x2 2x3 S 400 n my x1 gnu 2 6 a 5 y1 50y1 600 300 400 x2 3 m1nTaTay2 67y2 600 300 400 x3 3 111175757W3 75y3 xl 2 0 z39 123 xl integer 139 123 yi binary 139 123 a The expected time and variance for activity E are 2 and 011 respectively b C d The critical path is A 9 D 9 F Activities A D and F are critical activities The expected time to complete the project is 22 days and the variance of the completion time is l The probability that the project can be completed in 21 or fewer days is 05 03413 01587 1587 7 Decision variables Yi of weeks actiVityi is reduced i A B Xi Start time of activity i i A B F Min 20 YA 15 YB 20Yc 10 YD 125YE st XBZXA10YA XCZXB8YB XDZXA107YA XEZXD77YD XFZXC107YC XFZXE107YE XF3 S 26 YA 2YBSZYCS3YDSIYESZ Xi Yi 2 0 Multiple Choice Questions 1c 6b 2b 7d 3c 8d 4d 9c 5c 10c 11c 12c 13d 14b 15b 16c
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