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Solutions of Problems1.10Last YearThis YearChangePercent ChangeLabor hrs.= 7.7%Capital invested= 20%Energy (btu)= 10%Productivity of capital did drop; labor productivity increased as did energy, but by less than the anticipated 15%.1.131500 125 = 18751.14(a)Labor Change:Percent Change: 0(b)Investment Change:5.6Assembly Chart for the ballpoint pen.Alternate Assembly Chart for the ballpoint pen.5.7An assembly chart for the eye-glasses is shown below:5.8Assembly chart for a table lamp.6.6Partial Flowchart for Planning a PartyThere are many forms of flow charts. Students can use a “top-down” approach like this, or place all the major activities across the top line without details.6.9Depending on the type of student body, the response could vary. A typical chart might look like the following:6.12Recommendation: Start improvement by focusing on the high-frequency items (i.e. parking, pool, etc.)S6.8 (a)TimeBox 1Box 2Box 3Box 4AverageRange 9 am 9.810.4 9.910.310.100.6010 am10.110.2 9.9 9.810.000.4011 am 9.910.510.310.110.200.6012 pm 9.7 9.810.310.210.000.60 1 pm 9.710.1 9.99.9 9.900.40Average10.040.52n = 4. From Table S6.1, A2 = 0.729, D4 = 2.282, D3 = 0.0.(b)The smallest sample mean is 9.9, the largest 10.2. Both are well within the control limits. Similarly, the largest sample range is 0.6, also well within the con-trol limits. Hence, we can conclude that the process is presently within control.(c)One step the QC department might take would be to increase the sample size to provide a clearer indica-tion as to both control limits and whether or not the process is in control.S6.15 (a) The total number defective is 57.(b) The process is out of control on the third day (of the next 3 days).Nine returns are within the control limits; so this many re-turns would not be considered unusual.The Cp tells us the machines variability is acceptable relative to the range of tolerance limits. But Cpk tells us the distribution of output is too close to the lower specification and will produce chips whose lives are too short.S6.31Upper specification = 3.15, Lower Specification = 2.85Since a value of 1.0 gives 2.7 defects per 1000 units, this means that the process is doing slightly better due to the fact that the Cpk is slightly larger than 1.0. This indicates that the process has at most 0.27% defective. Therefore, more than 99.73% of the bottles meet the specifications.7.1(a)A fun topic, as students will add a lot of waiting. Flow is, of course, dependent upon the school, but usually.(b)Flow diagram for a car wash:(c)Flow diagram for a shoe shine (customer perspective, a very different diagram would be prepared for the operator).7.27.3Time function map of a shoe shine7.4A service blueprint for a shoe shine. (For a discussion of this particular application see G.L. Shostack “Designing Services that Deliver,” Harvard Business Review 62, no. 1, (Jan.Feb. 1984):S7.9YearXYX2XY1996115.00115.001997215.50431.001998316.25948.751999416.751667.002000516.902584.502001617.2436103.442002717.5049122.502003817.3064138.402004917.7581159.7520051018.10100181.00SX =555SY =5168.29SX2 =5385 SXY =5 951.34Regression OutputConstant15.11X Coefficient0.312Std err of Y est0.301R squared0.9168No. of observations10Degrees of freedom8Std err of coef.0.033Year 2006 = a + bx11, therefore15.11 + 0.312 11 = 15.11 + 3.43 = 18.54,or 18,540 lensesYear 2008 = a + bx13, therefore15.11 + 0.312 13 = 15.11 + 4.056 = 19.17,or 19,160 lensesYear 2010 = a + bx15, therefore15.11 + 0.312 15 = 15.11 + 4.68 = 19.79,or 19,790 lenses(a)2006 capacity needs = 18.54 thousand2008 capacity needs = 19.17 thousand2010 capacity needs = 19.79 thousand(b)Requirements in 2010 are for 19.79( 1000) lenses. Therefore, Eye Associates will need 8 machines (19,790/2,500 = 7.9, round up to 8).S7.10In 2006, Eye Associates has 8 machines 2500. In year 2011 it needs capacity of 20,100.(a)Therefore, if it adds 3,000 to capacity in 2006, total capacity in 2011 will be 23,000 lenses, more than adequate. Exceeds by 2,900.(b)If it buys the standard machine in 2006, its capacity in 2011 will be 22,500 lenses, still more than adequate; the smaller machine will suffice. Exceeds by 2,400.8.5Crestwood is best.SiteMaitlandCrestwoodNorthside MallFactor(weight score)(weight score)(weight score)Land space182124Land costs1020 7.5Traffic density101612Neighborhoodincome 7.5 10.5 6Zoning laws 8 2 9 Totals53.569.5 58.5So the local supplier is best from 0 to 4,800 units. A is best from 4,800 to 8,000 units; B is best from 8,000 to 13,333 units; and C is best above 13,333 units.8.19(a)ProfitBonham = 800,000 + (29000 14000)X= 800,000 + 15000XProfitMcKinney = 920,000 + (29000 13000)X= 920,000 + 16000XCrossover is where ProfitBonham = ProfitMcKinney;or 800,000 + 15000X = 920,000 + 16000XCrossover is at 120 units.(b, c)McKinney is preferable beyond 120 units, Bonham below 120 units.(d)Bonham has break even at about 53 units; McKinney about 58, so both are beyond break even at thecrossover.8.21The distance-minimizing location is at (5.95, 4.35). This minimizes distance traveled, but is “straight line,” which does not reflect realities of highway routes. It does not consider rivers, bridges, and other geographical impediments. Consider placing the office as near the center of gravity as possible and still be on or near a major highway. Students who overlay this onto a map of Louisiana should recognize that Baton Rouge would be an ideal location.9.1Interstation Activity MatrixPickupPickupVerificationPaperworkAdvisingClassof Statusand FormsStationCardsand Payment(A)(B)(C)(D)Paperwork/Forms (A)045055050Advising (B)35002000Class Cards (C)000750Verification/Payment (D)0000Interstation Distance Matrix-Original LayoutPickupPickupVerificationPaperworkAdvisingClassof Statusand FormsStationCardsand Payment(A)(B)(C)(D)Paperwork/Forms (A)0306090Advising (B)3003060Class Cards (C)6030030Verification/Payment (D)9060300Load DistanceA B:450 30 =13,500A C:550 60 =33,000A D:50 90 =4,500B A:350 30 =10,500B C:200 30 =6,000C D:750 30 =22,50090,000Initial layout:Interstation Distance Matrix-Improved LayoutPickupPickupVerificationPaperworkAdvisingClassof Statusand FormsStationCardsand Payment(A)(B)(C)(D)Paperwork/Forms (A)0303060Advising (B)3006090Class Cards (C)3060030Verification/Payment (D)6090300Load DistanceA B:450 30 =13,500A C:550 30 =16,500A D:50 60 =3,000B A:350 30 =10,500B C:200 60 =12,000C D:750 30 =22,50078,000Improved layout:9.14Performance TimeTask Must FollowTask(in minutes)This TaskA0.1B0.1AC0.1BD0.2BE0.1BF0.2C, D, EG0.1AH0.1GI0.2HJ0.1 IK0.2 FL0.2J, KM0.1L1.8 or Efficiency = 90%(d)Idle time = 2 min per cycle= 2 min. 12 cycles per hour= 24 min. per hour9.15a)Takt time = minutes available per day/units demanded per day = 420/250 = 1.68 minutesb)Number of cross-trained employees = (1.1 + 1.1 + 1.7 + 3.1 + 1.0)/1.68 = 8.0/1.68 = 4.76 5c)The cleaning operation is substantially longer than the others so it warrants special consideration to ensure that a smooth flow can be maintained. A machine constrained task or lack of cross-training may suggest that more traditional assembly line balancing techniques be used.9.16Performance TimeTask Must FollowTask(in minutes)This TaskA5B3AC4BD3BE6CF1CG4D, E, FH2G28The work activities may be grouped, however, into no fewer than five workstations without violating precedence requirements. or Efficiency = 80%Several other balances are also possible. One of them is to place A alone, tasks B and C together, D and F together, E by itself, and G and H together.12.13(a)(b)(c)(d)(e)(f)ROP = dL = 10(2) = 20 units (where 10 = daily demand)12.17Production order quantity, noninstantaneous delivery.(a)D = 12,000/yr.H = $.10/light-yr.S = $50/setupP = $1.00/lightp = 100/day= 4,472 lights per run(b) (c)(d)Total cost (including cost of goods)= PD + $134.16 + $134.16= ($1 12,000) + $134.16 + $134.16= $12,268.32/year12.23D = 20,000/yr.I = 20 percent of purchase price per year in holding costs, where H = IPS = $40/orderP = $20/tire if fewer than 500 are ordered;$18/tire if between 500 and 999 are ordered; and$17/tire if 1,000 or more
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