HW#2.2010W.sol - COMMERCE 290 HOMEWORK #2 Complete by:...

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Unformatted text preview: COMMERCE 290 HOMEWORK #2 Complete by: September 30, 2010 This homework is for practice only and is NOT to be handed in. However, students should have completed this by the date indicated above Note: As you know from the course outline, some homework assignments are completed individually and others are completed in groups. This homework is to be completed by individual students only. Students are reminded not to work in groups, not to discuss your homework with others and this includes using the Course Discussion Forum as a means of communication for this homework. This is NOT a group work homework. DIRECTIONS: 1. For Problem #1, write all your answers in the indicated spaces and show all work on this paper. No additional pages will be accepted. For Problem #2 and 3, please staple the pages to the end of Problem #1. 2. Show all work on this homework paper. No credit for answers only! 3. Be sure to include your units in each answer. éa iu‘i‘t/M I Last Name: ' First Name: Student Number: Signature: Excel Lab Number: Problem Maximum Possible Marks Awarded 37 Problem 1 (37 marks) Save—On Taxes is a Vancouver firm specializing in preparing Canadian lncome Tax forms for their individual and corporate clients. Save-On processes only two types of income tax returns; the T-1 Return for individual clients and the Corporate Return for corporate clients. Each return, whether it is a T-1 or a Corporate Return, is checked by three separate departments within Save-On Tax. These departments are called the Deductions, income and Arithmetic departments and have respectively 1,168 hours, 952 hours and 362 hours of labour hours available each processing cycle. Returns not completed during one processing cycle are completed during the next processing cycle. Management requires that the company process at least 25, T-1 Returns each processing cycle. The profit contributions for each T-1 and Corporate Return processed by Save-On Tax are $10 and $20 respectively. A complete and correct formulation and an incomplete graph are shown below. Using the following decision variables: T = number of T-1 Returns to process each processing cycle C = number of Corporate Returns to process each processing cycle answer the remaining questions below. max Profit) 1OT + 200 st Deductions) T + 9C <= 1168 Income) 4T + 5C <= 952 Arithmetic) 2T + C <=362 MinDem) T >= 25 Non—Negativity T, C >= 0 (a) (1 mark) In the Deduction constraint, describe what the “9" measures. I 53¢“ COVPVV>+6 wé'fi/rt/L ‘l‘zK-cs fl (4&an M W (b) (2 marks) The Boss at Save -On Taxes has said that the company should only prepare Corporate returns since each Corporate return translates into $20 profit, whereas each T—1 Return only provides $10 per return. Without referring to the, yet unknown, optimal solution, how would you respond to this argument? 1/‘3&$§ :5 lynarqu 1466464 “4/ Dan I144) Artrt’tv Page 2 of 8 (C) (5 marks) The partially completed graph below correctly identifies the Deductions constraint and eitherthe income or Arithmetic constraint. (l) Add any missing constraints. (ii) Label all the constraints by name. (iii) Shade and identify the feasible region. (iv) Draw and identify the iso-profit line on this graph showing where the optimal solution is located. (v) identify at which intersection the optimal solution exists. MW DEM ? Arum 180 2160; 17m: §a7l~. I— ; 1407; n: 1 ‘ Dedictions m I / *5 ‘ / 3 100 J \ U 5 \ réfl Page? “5 sol f/FR =11: 40* ‘ I / 20 I Cé‘fiag O 7' l7 V" l I V ’ V ‘ 7 l7 V V 7 < l H 0 20 4O 60 80100120140160180203220240260 #of T-1 Retw'ns (d) (2 marks) Save-On management is hoping to produce 120 T-1 Returns and 110 Corporate Returns the next processing cycle. Comment on their plans. I Wfl+ P09511016 ‘ au+§LJéL PK ) WM Wu.- Page 3 of 8 (e) ( 2 marks) What is the optimal solution? 1337+ 01¢ :. we? =5 wT—r‘BOC‘ 407’?“ I)*T+5&= “[52. :5 “T4' g‘: 4”" 3! z, :: 31-20 #7 Your Answer: (f) (1 mark) lfthis problem was formulated in Excel, what would be the value of the target cell? MAX mT-i- Zia lob”) 4.2061sz 5; Your Answer: 3‘ 2' 9 p (g) (1 mark) How many hours will Save-On use in the Arithmetic Department? A) 2T+¢=? 2(79 + :20 :2 20!? 2447 (4009‘) Your Answer: (h) (2 marks) What is the allowable increase and allowable crease for the Arithmetic constraint? - Allaw ‘5 NW” A) 2.1“? (/5 392- 1(79) +1257: 24% 67¢ Your Answer: Page 4 of 8 (i) (J) (k) (3 marks) FOR THIS QUESTION ONLY, suppose the MinDem constraint was changed so that the minimum was now 40 units. {Circle the correct responses.) No (I) Would the feasible region change? (ii) Would the optimal solution change? Yes (iii) Would the set of binding constraints change? Yes GI? (4 marks) Determine the allowable increase and allowable decrease on the objective function coefficient for Corporate Returns. ,L{ L —10 4 -.__L f . A; at _. q A. ---i& “.12 .5: "J" ‘2’ H 721 '6; a! ‘1‘ > L2. x(r£z> (4433.12 ,2 -—L 2:67 6‘) ‘2’ «62, 2 0‘ Lf¢z 2 {0 010 3 '6’; ,cz ,2 12. 50 z ’6 5' an Alltu/ 1‘ = 9'” 12, {0 -— 2 ‘5 g 9‘ { Allrw " ’ YourAnswer: (3 marks) Determine the allowable decrease on the Income constraint. , Mpvt 'lv Your Answer: Page 5 of 8 (l) (4 marks) Set up, but, DO NOT SOLVE, all the equations you would need to determine the shadow price for the Deductions constraint. DO NOT SOLVE. s. l b\'r+qc H994 % mum-rm = “’3’” paw Pfd¢t+ “1 "6‘ -. a (J Puflpl+637r5¢> ancl : 51/»;Jyu/ P/lC/é (m) (4 marks) The Save—On problem was correctly formulated and solved in Excel with the following partial sensitivity report output. Decreas Increase R H Side Ded Outputw _ ’ Inc Output Suppose Save-On can secur up to an additional 600 ours in either the Deductions or Income department, but not be . In which depart ent, Deductions or Income, would you recommend purchasing extra time? Circle the cor ect response and provide convincing evidence. " ' Deductions lncome Evidence: WZ/ 0&‘4 54" flwaM W 7yal°141 kept“ (WW 5+‘vam’l‘s Reva sl/wclvd/ Pond; :fl wéyymcl «f’cuélf Alba” *1 5'1 V14”9+ / Ana/we W Wm tux/‘1: CW we Oine'b’m’r. 13> . 49?? x I) 34mg, : 7/3??.‘78' 2.2;?! x Ila/37"}: fi£?/a cum” :3) sumo {WW/l? 7 flex. :1? Page 6 of 8 (n) (3 marks) FOR THIS QUESTION ONLY, suppose revenue and cost savings could be realized that would change the objective function to Max 20T + 100 (from the current Max 10T + 200). What effect(s) , if any, would this change have on the optimal solution? No calculations are required. , Wax/u pp+zMe( 9&[u’hfl‘4 (ti/164% an swag 05% 14M 7V2PI/ZH’I7 4415 néw 190 prawn-F (two Please do not write below this line. Page 7 of 8 Problem 2 ( 43 marks) Use the Textbook Problem 61 (Chapter 4, Steelco) to answer only the following questions: Hint: Please note that you are determining how to minimize the cost of producing ONE ton of steel. (a) What are the two decisions that need to be made? (b) What is the objective or target for these decisions? (c) Set up the above problem in Excel using the style that we used in class. Make sure that your spreadsheet model is logical, well organized and easy to understand. in building formulas, use the sumproduct function where appropriate. (d) Solve the problem using Solver. What would be your recommendation to management in terms of the decisions that need to be made? (e) What will be the Total Cost of producing 5 tons of steel? (f) After observing the model and its solver output, (1) What is the tensile strength of the finished steel? (2) Which constraints are binding? (3) What is the percentage of nickel in the steel produced ? (Q) There was a requirement that it was necessary to produce 1 ton of steel. if that restriction was removed from the problem, would the total cost increase, decrease or stay the same? Explain. (h) You will notice that the Solver model shows a decimal answer for several of the changing cells. Briefly comment on the correct way to interpret these decimal numbers. (i) Place a text box on your model page which includes information regarding the optimal decision. (j) Print out your spreadsheet model on one page in landscape orientation and include it with your answers. (k) Print out the cell formulas on one page in landscape orientation showing Row and Column Headings and include it with your answers. (1) Formulate the above model algebraically. Be sure to clearly define your decision variables and show your complete linear programming formulation. DO NOT SOLVE. Problem 3 (10 marks) List (but do not describe) the four reasons given in the textbook for studying management science. Page 8 of 8 Question 2 ( 43 marks) Steelco, Question 61‘, Chapter 4 (a) The 2 decisions facing Steelco are: How many tons of Alloy 1 to use in the production of 1 ton of steel How many tons of Alloy 2 to use in the production of 1 ton of steel 2 marks (b) The target is Minimize Total Cost (Total Cost) } 1 mark c) See attached Model2 } 10 marks (d) The 1 ton of steel should consist of 62.5% of Alloy 1 and 37.5% of Alloy2 or 625 pounds of Alloy1 and 375 pounds of Alloy2 2 marks if students assumed that the tons listed in the problem were metric tons, then pounds would be replaced with kilograms (e) $968.75 ($193.75 x 5) } 1 mark 0‘) (1) 45,000 psi 1 mark (2) There are 2 Binding constraints: Tensile Strength and Amount produced must equal 1 ton 1 mark (3) 1.1875% 1 mark (9) Total cost would DECREASE to $0.00 2 marks because this constraint is binding 1 mark and removing it makes the constraints easier to meet, therefor less cost 1 mark (In this case, you would produce no steel to achieve min cost) (h) Decimal numbers are OK because # tons needed can be fractional 2 marks There is no practical reason to restrict the changing cells to be integers (i) See Model2 for textbox ] 1 mark (j) See Model2 } 2 marks (k) See FormulasZ } 3 marks (I) See Sheet: Algebraic Formulation } 12 marks; see mark breakdown on alg formulation sheet Question#2 N Eco—>— N as .322 68:5 >o=< 90 9:30: mwm u:m F >o=< £0 955953: 6:92 V mg: 9 u9moo=m mo Esocm {9: F “1 90 8:30: mmm x_.E 9 80: c :9: xo9x9 v 9: 9 n9moo=m 0: 2:05 {9: F .. 30> 69m 3 :9 F 839: 9 53:8 992:9 95 6mg 6 mo 26% $9 ucm gmme 99 30> E 8993:: 36mm .umN_:m9o :95 2 598. 6:9: :69 t. 28E Em 903nm: HOZ om « .N >226 90$ 95 86 2228. 962m :68 9.2952 F >o=<5 9.0% 5.: 9 umm: mEom mm: 6: on 95an : {m8 Co E:E_me m U:an « 20> 69m 3 :9 F 82:05 oh 99:0: :_ 99%: m_ g : VtmE F Baum: - a :9: mgmumu:m_ :_ mama m9 mczcta 63.29 929: 52980 .9530 N + 8 t9: BUOE BBQ 9: :9 mme or £53 2 «mmcm 2E, * 3 tan. 53:0 9555. m:9 mde mmod 69w “5 :9 r 9 mSQE =28. N 22 F 22 :2: :32 69m *0 :9 v 83:05 62.: 30> 2 9V :3 908: 5965 25:8 $99588 mmod Nmod :oEmo Ememn. wm9:m8ma N56 wood .32: Emema $9588 mmod 9.0.0 :oo___m E851 EmEESUmm EmESSgK .282 68.2 x92 :__>_ a: E. . om Nv :3 908: £995 288 $9588 mhmmo a .. fioé o\oo.m :oEmo E85: wmscmemg £9 5 a $3 $0.? 6on 286: mmmzmemg 99 No Q "NOON §N :83 E86: 8: 59:0 5: mhmmw m 88 8; c9 :8 58 .282 E82 6.82 58 N 32 P 32 522 E:E_E—2 .30.... 9mm. 52:. :m 5:330 .v 5520 <29 863m Nu £28.: an $8583 $9383 $9588 Vmwum.m_ Cu wwwimL—Un vmwgmb— an $33 gamma—u Im:u§:r&&§3mu .vaqu Emcee—o oFawkwiaaigrzimu émmom ummmmau mQCQDQCIaEDmH Emmum qwmmmau snubnnigwwiqhnmu N 85:5; mqmomucfi E 2:55 8: 2 695 : VtmE F Gamma ,, .63ch 8: oo 20 En UsuEaEzm :9: 650 222:8; « :mw .wonwmvHODQOmQEDm “w E230 Em mmSEE 9:: mme N B E:E_me m 63% g ESP E mme m 2:03 m_ 3.3 micte w_£ v6 mEEta wE._. ., v. tan. 52:0 9.255. in $95er $95qu mmmEmSma mmod Nwod mood mmod wro‘o BEBEcmEmEBScww EUOE Etc—2 xms. :__>_ Nmod emf??? on Rm??? :3 8.0 33$; a” 23 5.0 5.33:7 $3 8.0 Sm ..a“.3333”.“395200522? 8m o? BB: 58 N 52 F >22 Eggs: :28 «a case". I H. cozmSEBu 93mm? 0 HA N< €< N< + r< mmo. nv N<vo. + w<mo. Nro. nv N665. + _‘<ro. mNo‘ nv N<mNo. _‘<No. mv HA N<om. r<Nv Nmo.nA N660. E60. £08 9.55 19:9: m moo. “A «<20. + 25 m5: “A N<mmo. + _‘<No. H9 “$.3sz $58 + $39 SEES 62w 6 :9 V E NE? 6 ea 2 6% B :9 V 5 :22 B x. 2 mo wvtmE N 6me Lo :9 r 5 Sn 9 ~32? ho mac“ “n n m< 6% B :2 r E :a 9 :22 B 22 3, u E m: 8285 .v 3320 .8 .5325 <va gasses“. 295mm? Question 3 ( 10 marks) List ( but do NOT describe) the four reasons given in the textbook for studyingmanagement science. Answer: 1. Development of Logical Modeling Skills 2. Development of Quantitative Skills 3. Development of Spreadsheet Skills 4. Development of Intuition Source: Page 15-16 Custom Publication for Commerce 290 Marking key: 10 marks Although we would expect that students would understand the details under each of these steps, this question asks them only to "list" the 4 reasons, not provide explanations, descriptions or details. if they do provide correct details or explanations, do NOT deduct any marks. Question 3 ...
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This note was uploaded on 01/19/2011 for the course COMMERCE 290 taught by Professor Brianogram during the Winter '09 term at The University of British Columbia.

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HW#2.2010W.sol - COMMERCE 290 HOMEWORK #2 Complete by:...

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