1-19 managment statitistics and problem sets

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1. the operator of a flight school desires to predict the number of students for the coming year so that he can contract for fuel, instructors, a/c, etc. the school has been in operation for one year. the enrollment data for that year, starting in january is presented below. a. from among a three month moving average, four month moving average, trend, and seasonally adjusted trend, chose a method that appears to best predict the monthly enrollments for the next year, assuming that flight school may grow unbounded. b. explain and justify the method used for the forecast. 40 42 48 52 56 60 61 61 56 56 55 54

2. the following data concerns fuel sales by a distributor and is given in thousands of gallons. case i case ii case iii jan 15 12 12 feb 17.5 15.5 15.5 mar 20 19 19 apr 22.5 23.5 23.5 may 25 27 27 jun 27.5 30.5 30.5 jul 30 33 33 aug 32.5 34.5 34.5 sep 35 36 36 oct 37.5 36.5 36.5 nov 40 38 38 dec 42.5 39.5 39.5 jan 45 42 43.5 feb 47.5 45.5 46.5 mar 50 49 49.5 apr 52.5 53.5 53 may 55 57 56 jun 57.5 60.5 59 jul 60 63 61.5 aug 62.5 64.5 63.5 sep 65 66 65.5 oct 67.5 66.5 67 nov 70 68 69 dec 72.5 69.5 71 a. for each of the cases predict the fuel sales for the next twelve-month period. chose the prediction method that you think will give you the best prediction. briefly describe the prediction method used and your rationale for selecting that method.

3. a manufacturer of aircraft components is concerned about production variations and asked that his operations researcher determine the factors contributing to varying production rates. various supervisory personnel were queried about the causes. chief among their thoughts as to the cause were: the number of employees actually on the job the in-plant temperature the in-plant light level and the percentage of time actually on the production floor by supervisory personnel. in an effort to determine the probable cause(s) of the fluctuations in productivity and to attempt to produce a predictive means the following data were collected: attendance is in percent full manning. temperature is in degrees f. light level is in units of percent of maximum supervisory presence is in percent of maximum. day production employee attendance plant temp plant ll supervisory presence 1 110 105 72 100 100 2 95 100 82 100 100 3 100 95 74 95 95 4 98 99 76 98 98 5 92 95 84 96 94 6 91 96 86 95 93 7 89 98 86 94 93 8 91 99 87 95 95 9 88 98 87 95 94 10 88 98 88 99 100 11 90 101 86 97 99 12 92 100 85 96 95 13 94 100 80 100 97 14 105 102 78 99 98 15 106 101 77 100 98 a. which independent variable best predicts the dependent variable, production? why do you so state? b. using attendance as the only independent variable, predict production if attendance is 75, 93, and 112. which of these predictions is likely to be the most valid? why? c. progressively build a prediction model using as many of the independent variables as you see fit. how good is the model? (how much of the variation in production does the model "account for"?) what is the range of predictability or usability for each of the independent variables used?

4. avair, a regional airline, reported miles flown data as shown in table 1, below. in january 2002 avair added aircraft to its fleet and changed the method of scheduling maintenance. revenue seat miles (000's) available seat miles (000's) 2006 2007 2006 2007 january 10,584 13,330 16,100 18001 february 11,100 13,900 16,040 17940 march 11,500 14,145 16,010 17,932 april 12,050 14,895 15,900 17,920 may 12,550 15,110 15,890 17,898 june 12,910 15,892 16,025 17,863 july 13,180 16,100 15,925 17,810 august 13,100 16,010 15,843 17,765 sept. 13,106 15,991 15,861 17,722 october 12,900 15,900 15,832 17,660 november 13,001 19,952 15,815 17,625 december 13,050 16,012 15,804 17,540 a. review the data and suggest area(s) where problems or discrepancies may exist. b. which forecasting method, from among those discussed in the text and in class, best predicts revenue seat miles (rsm), and available seat miles (asm)? justify your answers. c. if no additions are made to the avair's fleet or practices, when do you predict that avair will no longer be able to increase revenues from passengers? assume that non-revenue passenger miles are 5% of revenue miles.

5. you have the opportunity to expand your specialty freight business by purchasing or leasing an additional aircraft. you have determined the most suitable type of aircraft is a shorts airvan. you have calculated the increase in net profit over the next three years with this aircraft for five estimates of industry activity: rapid growth moderate growth slight to no growth slight decline and moderate decline if you buy, your estimates of profitability increase are, respectively: $200k $100k -$40k -$80k -$150k if you lease, your estimates are: $100k $50k -$20k -$40k -$60k of course you have the option to do neither. a. if you have no good idea of the future of the market and you wish to make the choice that will maximize maximum profitability you will chose to_____________? b. if you wish to chose the alternative that will minimize possible loss you will__________________? c. if you estimate, based on your observations of the industry climate, the following probabilities for business growth; rapid growth .1 moderate growth .3 slight to no growth .3 cline .2 decline .1 which alternative is indicated?

6. you are the owner/operator of a medical electronics firm in the early stages of operation. you have just concluded a deal with an asian manufacturer of hand-held blood glucose measuring devices bearing your brand name. you can market this receiver at a highly competitive price. your potential profit for various purchase levels under each of the five possible market conditions is shown in the table below. potential profit table market condition categories quantity 1 2 3 4 5 10000 100 110 120 135 140 15000 90 120 140 155 170 20000 85 110 135 160 175 25000 80 120 155 170 180 30000 65 100 155 180 195 35000 50 100 160 190 210 40000 45 95 170 200 230 45000 30 90 165 230 245 50000 20 85 160 270 295 *profit in thousands of dollars with no knowledge of the probabilities, how much would you stock? why? if you think each scenario is equally likely what would be the best stocking policy? in an effort to reach a decision on purchase and stocking you have obtained the following information from a compilation of reports and articles in trade journals. you classified the market in five categories from worst to best (1-5). probabilities for having each category of market were estimated as follows: category 1. .10 2. .20 3. .50 4. .10 5 .10 a. given this information, what would be the best stocking policy? b. what is the expected value of perfect information for this situation? c. if new information causes you to revise the probabilities for market condition 2 to .28 and market condition 5 to .02 would you change your decision? if so, how would you change it?

7. your company manufactures turbine blades for engines in production batches for each type. for one type of blade, the a39t, you have an annual demand of 10,000 units. it costs you $1000 and takes four days to set up each manufacturing run. holding (storage) cost is $0.50 per unit per year. once production is set up, 80 units can be produced per day. daily demand rate for the units is 60 per day. a. what is the most economical number to produce per production run? b. how long is each production cycle? c. how many days, exclusive of setup time are you manufacturing a39t blades? d. what is the annual holding cost?

8. you buy tow hitch balls in large lots for the tow tractors you manufacture. you estimate that it costs you approximately 20% of cost to store a ball for a year. ordering cost is estimated to be $49 per order and your annual demand is for 5000 balls. your supplier offers you the following price schedule: quantity discount (%) discount cost 0 to 999 0 $5.00 1000 to 1999 4 $4.80 2000 or more 5 $4.75 the discount cost is for all balls in the order. you operate 5 days per week, 52 weeks per year, minus 7 paid holidays. a. what price per ball should you pay to minimize total cost? b. how many balls should you order at each time? c. how many orders will you make per year? d. what is your total cost for balls each year?

9. slixtrix conversions, located in waldo, florida specializes in conversions of pick-up trucks and vans. in particular, they do a very good business in their signature line of each. the business has three production shops which, using good project scheduling skills, work on the vehicles simultaneously. the shops are: preparation upholstery and electric/electronics. the company nets $5000 for each truck and $6000 for each van produced and sold. the work requirements for each, in hours, and personnel available are given in the table below. personnel work 8 hours per day, five days per week on the conversions. shop trucks vans personnel preparation 8 12 10 upholstery 10 8 8 electrical 12 16 12 the company has standing orders for 12 trucks and 10 vans per week, and is able to obtain parts for only 20 vans per week. a. how many trucks and vans should they produce each week to maximize profit and remain within the stated bounds? b. what shops or other constraints determine the optimum solution? c. are any shops over staffed? if so which ones? if people from an overstaffed shop were able to work in another shop, would transferring any from that shop improve profitability? (how many, from where, to where?) mandatory question

10. consider the production, sales inventory, and capacity limits stated below for the manufacture of small turbine engines used in auxiliary power units, ground support equipment and various other uses. the company expects to market the unit for $50,000 each in quarters one and two and to raise the price to $55,000 for the third quarter. at that price it is expected that demand for the three periods will be 250, 300, and 300 respe
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