290 last year midterm - THE UNIVERSlTY OF BRITISH COLUMBIA...

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Unformatted text preview: THE UNIVERSlTY OF BRITISH COLUMBIA Faculty of Commerce and Business Administration COMMERCE 290 MIDTERM EXAMINATION October 16, 2006 PLEASE READ THE FOLLOWiNG: 1. This examination consists of 13 pages including this cover page pius 2 pages of Excel printouts, Please check to ensure this paper is complete. 2. No candidate shall be permitted to enter the examination room after the expiration of 1/2 hour, or to leave during the first ‘A hour of the examination. Candidates are not permitted to ask questions of interpretation. ie: “What does this mean?” 3. Cell phones must be turned off and are not permitted to be in view or be used as a watch during this exam. 4. Detailed work must be shown to receive credit. Show all work for non-multiple choice questions on this exam paper in the space provided. No credit for answers only! 5. Time: 100 minutes 6. CLOSED BOOK EXAM; Non— graphing, non-programmable calculators permitted (graphing calculators like the Tl 83 etc are not permitted). LAST NAME NGSM FIRST NAME [Hr-if“ k : SIGNATURE EXCEL LAB SECTION L— i Maximum Possible Marks Awarded 35 i 1 * Note: Problem #4 for this exam is out of 35 marks and is completed in the computer lab HA 409 during this week. Problems 1,2,3 and Problem 4 are weighted 90% and 10% respectively. Problem 1 ( 35 marks) Telco produces both a cell phone and a standard phone for the national market. Both phones pass through assembly, electronics and testing which have respectively 320 hours, 720 hours and 200 hours available each week. Cell phones require 1 hour in assembly, 4 hours in electronics and 1/2 hour in testing. Standard phones require 2 hours, 1 hour and 1 hour respectively in assembly, electronics and testing. Due to contractual obligations, at least 30 standard phones must be produced each week but, due to limited storage space available, no more than 140 standard phones can be produced each week. Profit contributions are $10 for the cell phone and $12 for the standard phone. Let C denote the number of cell phones and S the number of standard phones produced each week. A linear programming model for this problem has been correctly formulated below: MAX 100+1zs fit?“ W t “’f A ASSEMBLY) C + 2 8 <= 320 m l ,3, T 4 C + S <= r C K j C TESTING) o.5c+s <= 200 e f0 s + lZ u ~-' ' ' 5%."? 5.5.3 DEM) s>= 30 a 5 STORAGE) 8 <= 140 l— i - NON-NEG) C, 8 >= 0 (a) (5 marks) In the space below, all of the constraints (with “C” on the horizontal axis and “S” on the vertical axis) have been provided. Label all the constraints by name and (l) clearly shade and identify the feasible region and (ii) draw and identify the iso-profit line on this graph showing where the optimal solution is located. and (iii) clearly identify at which intersection the optimal solution exists. .— -' .kl 250 I CLLCT o ' Page 2 of 13 (b) (2 marks) Briefly explain what the “2" coefficient in the ASSEMBLY constraint tells us? Zia “hm. shim-we. (nevi-Pé’grnsti C9 (c) (2 marks) What is the optimal solution? \ m \a 2(46 + 5} “(730) C.) 2;}: regs .jéOlZf’f xx“. /' 7C : HZO C :— IQO Your Answer: (d) (2 marks) You will notice that the minimum DEMAND constraint is exceeded. Why would Telco do this? We. OW (“chat/HM“ QNOVU 67)!er Wow 5 4a» G? (52A is?) e lira-tile” {DE/V: ii MEI? (it: is + we“: ones to 20 minutes Should they do this? Circle the correct answer and explain. / M Yes No Explain V 5: r 7 . "IL ~ :5 q Moll/l Emdmo} (Jon‘sfiwn, 'eSJme) Page 3 of 13 (f) (3 mark) Suppose Telco is currently producing 150 Cell phones and 85 Standard phones each week. An eager young manager has suggested that these production levels should be reversed since the profit contributions are $12 on the Standard phone and only $10 on the Cell phone. What advice would you offer Telco about this plan? Do fl0+ Clo +1413 PM" 3 h ..; J-t f ‘e- 5'“f¢¢?€5 CCDfli‘iévffl a fit aw min-r) W W mt Slim-“Md 4‘” i ‘ t. 3 n:- Elf-".5? b9? Profit/two l7 C" i“ -- =-‘”- f -' t * at. Wt H M 5 W“ Hm -./" t C E a; M Comet-rufflk 0'“ 5/ g , -( ‘ . r s c: M ,; (16,51? ( :3, 3- . w. n)!“- -:T '”' ft:- I {In ‘Wl ‘ ’tgg! j . .._/ ,l .‘__, (g) (4 marks) Determine the allowable increase and allowable decrease on the objective function for Standard phones Cl “C? M t. W F0 (O C 1‘ a Z S :1 ..4 z m < *1 _-' 2/ fl . 4 _. Z 4 4,134,; sneeze Cl 2 Z t. 5 I2 5 2c) ‘— 4 f 1?- ”,‘E 4 w) 2:; m (— c d 2. :21. “1:5 (1’ > a 2 / 5 Alfowablfi Marga-5a Lf' z'// 7-2“ "' 2‘5 {.2 ,4— 2’0 YourAnswer: A'HMWW“: "'£«F“t”"5f -' 1‘25 (h) (3 marks) Determine the shadow price of the ELECTRON constraint. 4 C r j 3' 72 U 4‘ I .. l, r .. (was? «I 12‘: » C J: 26 :3 32-0 f.“ mwwmw '74 1 ll 2 . Z I 2 mg“; Pam-fit to (146.2,???) g l2f7‘h'357) I Sé '14 5 ,5 g r. = ‘ a \.. ' _ 2;: if? I an: at ~54 lfléléoj 4/ {1(90V k JV“ if / ' YourAnswer: ! r I Page 4 of 13 (i) (2 marks) Determine the allowable decrease for the ELECTRON constraint. ‘Im Mr? 4 C r 5 “5—” LA/ Slicer?! cal“: , W at,“ C, + 2 :2 0‘ r \I‘ 4 f \ a 2 <3» :- l’l‘ 4O.)- / 4 .u/ ,ch C, : 40 r“ F” "' r c 4 5 :- 7 :2 r: ([0 r c — ,«EO ARK 1‘ g. I got") : Q . Your Answer: (j) (2 marks) What is the shadow price for the DEM constraint? What is the allowable / t "r (k) v l '\(\.CJ \- increase for this constraint? at C + S ; 7 Z 0 (3(0 5:5047f $53! 94 Z//4(# :3- 7’5’0 4Q: 6‘35? , 5721.25 6) ‘ r l Bu!" “3’ .z :21- ( c 50/ A New Cl r I'l-FWQ 5: ii? (3 marks) The objective coefficients for Cell and Standard phones are 10 and 12 respectively. For this question only, suppose that these numbers were changed to 6 and 12 respectively. What effect would this change have on the problem? +125 “10 _.__~— 4 r» l; "' i. 2 (l) (4 marks) For this question only, suppose the company is thinking of producing only one product; either the Cell phone or the Standard phone but definitely not both. This ' means, for example, that all the existing requirements for Standard phones would not apply if they produced only Cell phones and all the existing requirements for Cell phones would not apply if they produced only Standard phones. If they went ahead with this “one product only" plan, (I) What is the maximum number of Cell phones they could produce? Standard phones? .m’ J; a” I” V {— ‘(Cl VII riff“. Q’ Cy l 1!:- I o , no . l i O i " to.) “ (1; a 3 :3 a rec) <21 :3 lm g o 4:71 S ' 5 ' S a, a. , / , .t’. c— c I 535.3,} 2 [(500 [4'0( ,2). _- fégo (ii) Which phone type should they produce? Circle the correct answer and explain. ‘s/ Cell pho e/ may/Q s, ’l’ Standard phone / Explain: Please do not write below this line Page 6 of 13 Problem 2 ( 31 marks) Nets: The Sldwbéiow isi’ai iiiédifleid? reach; 0f? the TWOIPQrsdilCi: TWO'EMashihé-‘ipmblem done if? :Homeworké#3Ai5tfiisigterm we: main: difference thatithe 2companyai'ssnow interestsid in i - iMaximlzingéprdfit-lgnét' imizingéédstitéS'WaS=th ' " thérfiemewdrékfirdblemiéThe? greyigisegggprqbleiil (with; changes'to 7 _‘ timbers; éQaQnidéafirhéfnewfihfbrméfidn E. iregafdingi%6035f3);iCQtTlPiélaWiffiaicofredigli élifjof ESEI‘lSiliViNRepoflfisi. 3' . . . . , _ . . _.._._derstahflihisréw53d_.7; iglvsnfielew Qadilh'g—P 'lel’th efull : k. . . . .. . aprobl‘emi;:; 72:25 i if r- i : i - A company manufacturers two products (P1 and P2) on two machines (M1 and M2). The required number of hours of machine time and labour time needed to product each product is shown on the attached Excel Model. The cost (which includes both the machine time and labour time) of producing 1 unit of each product is also presented on the attached model. There are 140 hours on each of the two machines and there are 279.9 labour hours available. This month at least 140 units of Product 1 and at least 168 units of Product 2 must be produced. Also, at least half of the Product 1 requirement must be produced on Machine 1 and half of the Product 2 requirement must be produced on Machine 2 This problem was correctly formulated as a linear programming problem on Excel and solved using Solver. The solved model, with an optimal solution and correct Sensitivity Report, are attached. Use these printouts to answer the following questions. (a) (1 mark) What is the Total Revenue generated by this problem? cg @725 Your Answer: ‘ (b) (1 mark) Which machine. M1 or M2 is slower? Your Answer: Page 7 of 13 (c) (2 marks) Which Excel formula below is the correct formula to use to determine the value in C30? (A)=SHMPROD 'i'i: a_,, ...r .7 .m s + * (C) = (D) = C8*CZ1 + 08*022 + F8‘D21 + GB*D22 (E) = SUMPRODUCT(C8:D8,E21:E22) in.wa t “E. / E I 2'" Your Answer: ; J r . / (d) (2 marks) Suppose management had an opportunity to purchase up 10’le hours of either M1 time or Labour Time, but not both, at their regular costs? W' ' of these (if any) should they purchase? Explain. Z1918 OWE. both {Rim (e) (1 mark) Referring to the Sensitivity Report, show how the objective coefficient of 5.8 in cell F11 was determined. 3 - m” ) ,.. ‘t ,; m Ullr‘i ale. us 5‘”? 2 l 2—5) i 5‘" 4’ up (Q. s c: " l ‘f’: ' ‘ 5 6 t3 r if; {‘11 (f) (3 marks) Suppose the cost of M1P1 increased from $1.50 to $1.70. Would this force the optimal solution to change?§xplain. { Circle the best response }. Yes ® Don’t know Explain: I. , I, .H_ ~ y F {a {q “s. f; ,3" ." ;- i" "If " 2’1 ."35- .E r ,- FL “ I J; j I, —__-.K I = \ L . ‘ VA ._4 ‘1: u = . . “A, . I t ‘ _ r . f ‘ - 5'- '1' _9\ - _ . . ‘* ‘ Cit? ( a ti"; 2- i< r" r” site I ' / N b) l C {’7' 5 “9 H t, _; '4 _r y \J . .. _ I, l 4,7 H “I If 1.;.- in: _ Page 8 of 13 (g) (h) (i) (3 marks) You will note that the obj/active coefficient for M2P2 is -1. (1) Briefly explain what this wcyld’r’nean to management. f / - -\ : ins . . "3-" I If“ LC J: l .mv “"14 ' J ' {f \“u..«-—"' (ii) Given your answer above, why would this company produce any M2P2? C. {imfijff'gtiii’l’ ; Wit“ Predicts m“ he 2 6’: gi’d" v//fl~isbhsbg (3 marks) if Revenue for P1 increased from $8 to $13, would this force the optimal solution to change? Explain. { Circle the best response }. Yes No M Explain: w”- ‘i’ r.“- ktx: (9w i 0 [figs :3 "f a {574" i. h (is. p ’ i I fit? ‘ c! a :- r :59 1% [i Se ‘Trbf .4 ,r’ (4 marks) Suppose that an additional 30 hours (or nothing) of M1 time can be purchased at the regular cost. What can you say about the effect this change will have on: (I) the Target Cell? (07/) ’ //_/,..4. ‘ f f ‘f; rd“ Ettui§12i5 if * \_// (ii) Optimal solution. .! u"; I“ TA—L_\». VG l i "l L' 'k': I '3 .7; l sun r‘ 7f :lwsxr K \ Page 9 of 13 (j) (3 marks) Suppose that an additional 40 hours (or nothing) of M1 time can be purchased at a cost of $0.15 per hour more than the regular cost. What can you say about the effect this change will have on: (I) the Target Cell? (k) (3 marks) Suppose that an additional 50 hours of Labour time can be purchased at the regular cost. What can you say about the effect this change will have on: =_.’\.'i"‘.": aflewoélf zi}(v€‘f’SP (I) the Target Cell? é / _ “hi-“x V" v ,Jr— C& 3+ ‘1’ I I} \ r ‘ “dig: [Add/Hafirtak 3L hears wtl L .64 W V’/ H‘ .5 a“ W’amfiifp /_ 3 JV av‘é’lt‘iemfa G’wi‘rfi' :; v .r L f x: f't-t’fi'w J flaw Si arias) tilft,A/Mh ‘1 U" *1“ 1'” r: [fad if] (I) (2 marks) Suppose the minimum demand for P2 increased to 175. What can you say about the effect this change will have on: (i) the Target Cell? w i‘l’l/l M F? x/U (1‘0le- ih c: we, {-2 49 J/ 1/) I l .' / “*—- r Page 10 of 13 (m) (3 marks) Suppose the requirement that minimum production of P1 on M1 was decreased from 50 % to 40%. What can you say about the effect this change will have on: (I) the Target Cell? Vi OK [W6‘c7lrl (j: I?) 1; i” --.- v (ii) Optima/I,.solution. Explain L" Wrij/Ei/ ‘_ _ INCH/l L'ji-r-jiii-i'"? (c'flil‘fa’ { Please do not wn'te below this line. Page 11 of 13 A _E- Problem 2 — Two Products. Two Machines - s 1250 s 0.40 — - - 39/ s 4.00 _ EM I Revfunit $ 8.00 $ 3.00 —— i390 Minimum Production of Prod1 on Mach1 _ __ Minimum Production of Prod2 on Mach2 _- T : — — NNMN —-|—A-A-_l._t_L_\_L_\_\. 20 Action Plan Product1 _ .5}- _— _ M30112 “ —— _- _— _ — _ -- -- ' H 279-9 - ‘ I!“ i "‘ Problem 2 E H H H H Microsoft Excel 11.0 Sensitivity Report Adjustable Cells Final Reduced Objective Allowable Allowabl a Cell »- -- - . -~ - Value Cost Coefficient Increase Decrease El $C$21 ~ ach1 Prgucz. 110 o 6.5 1.6128 2.875 80821 MaafiTProduct 2 84 0 2.6 9.9387 1.7280 $C$22 Mach2 Product1 42 0 $D$22 Mach2 Product 2 84 0 ET“ 1.7280 1E+30 “"- Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $C$28 Mach1 Time Used 140 4.1071 140 47.04 _ 22.40 $01529 Mach2 Time Used 109.2 0.0 140 1E+30 30.800 $C$30 Labor Time Used 279.9 4.8333 279.9 46.20 14.40 $03531 DemandProd1 Used 152 0 140 12 1E+30 $03332 DemandProd2 Used 168 41.9693 168 12.9024 168 $C$33 MinProd1onMach1 Used 110 0 0 34 1E+30 $C$34 gnProdzonMachz Used 84 -1.7280 0 47.837 34.882 Sensitivity Report 1 it; Problem 3 ( 14 marks) Jack Mazzola is the owner of Dawson manufacturing and has contracted to deliver 800, 1200 and 1100 items in each of the next 3 months. The maximum production capacity of his plant is 900 units per month and the production cost is $20 per unit. Items not shipped at the end of the month in which they are produced must be stored and are assigned a cost of $3.00 per item per month based on ending inventory levels. Jack can also buy unlimited amounts of that item in the open market at a unit price of $21, $22 and $23 for months 1, 2, and 3 respectSVely. Jack currently has 50 items in stock but at the end of the 3rd period, he would like to have at least 75 units in stock. He would like to determine how many units to make and buy in order to minimize his total production, purchase and inventory costs for the 3 month period. (a) (2 marks) Draw a diagram which clearly shows all the details of this problem. i—E‘flU‘el‘fi‘ff'fl Is: 50 i I 2 $3 X. 1- t )_ _ “a New! “I T‘ThiM/‘Kfiig 5p:- 3’0‘0 [103 ll 00 ,iMni {pi-V U (THE) 5 T00 ._ QC- 3:45; K Erin; t'z/ “J: $- (b) (3 marks) Clearly define the decision variables that you would use for an algebraic formulation to this problem, which are consistent with your diagram above. Let ' ,/ I, ,— 554‘ 0F" {Ang‘Mfi n M». «a; (2+ @fld 01" I51" fl (View) \x \J T.“- M - if 94:7; .,. f 2/7."—‘"" .93 3 . A , ,t‘ W1 w. 1‘”qu l r W of “My”: ‘9“ H * f" 5/ a”: “ me P \ // (I: 2. R 5 u,— ” K // I? ("A ./ .e p - i ; Q, ' r“ J ,t - ' 1‘ ; , E: \\ I // 9 M \ i f: :2: 'Lk— / r ‘4 \ (c) "(3 marks) Using the decision variables you idenfified above, write the objective function \\ I foruthe owner’s linear programming problem. 0 FLAT“)? {1" w {fig-6 ll! “I; " I w ._ f “A in" 2:1 I I ~_ \7. M 1'; y] if r; 5 £— ‘1! \\\\ é KKK \L“ I: fist-— h-f— {LLme , 3, fl k d __. ._ R ' 7 + ’— E) A” 4” 25.5%; u I , :_...‘~-‘=' ' "I". ’1 .W -\.\\ I "I h r I. I. J/ l «i 2 JVXCE; t i- 233 “I has Rage 12 0f 13‘ t 22:7, +3.21??? 'Im" (d) (6 marks) Using the decision variables you identified above, list all of the constraints for the linear programming problem. Be sure to identify each constraint by name and indicate the correct units for each constraint (15M V1.96: atlm‘l’fl I; In if“ 327—) > C V, Kl {I R2 I R 2 i C? pet/MK'VLA Cd4$¥¥qu+ MET-3'35"? t' r' [DE/ide v 3 I“; [/3 ‘iJ-pl}':‘"1( o {of a; (:3 33%;}; g? \5' ‘7 ,/ a3 a.) Page 13 of 13 ...
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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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290 last year midterm - THE UNIVERSlTY OF BRITISH COLUMBIA...

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