Faaliyetler İş Araştırma ve İktisat Quantitative Part 1 Ekleyen: Murat y,ld,nm MARKETING APPLICATION MAN 203 QUANTITATIVE METHODS • (EMIL KUZEY LINEAR PROGRAMMING APPLICATIONS MAN 203 1_ The WIN BIG GAMBLING Club promotes gambling junkets from a large Midwestern city to casinos in the Bahamas. The club has budgeted up to $8000 per week for- local advertising. The money is to be allocated among four promotional media: TV spots, newspaper ads, and two types of radio advertisements. WIN BIG's goal is to reach the largest possible high-potential audience through the various media. The following table presents the number of potential gamblers reached by making use of an advertisement in each of the four media. It also provides the cost per advertisement placed and the maximum number of ads that can be purchased per week. - MEDIUM- - At! 01 E-NeE R EAe H "E-El (()ST PE R ADt$) MAXIMUM PER AD ADS PER WEEK TV spot (1 min) . 5000 800 . 12 Daily .Newspaper(full-page ad) 8500 925 5 Radio spot (30 sec prime time) 2400 290 25 Radio spot (1 minute, ahernoon) 2800 380 20 , WIN BIG's contractual ar-rangements require that at least 5 radio spots be placed each week. To ensure a'broad - scoped promotional campaign, management also insists that no more than $1800 be spent on radio advertising every week 2_ MSA is a marketing and computer re sea,rch firm based in Washington DC. that handles consumer surveys . One of its clients is a national press service that periodically conducts political polls on issues of widespread interest. In a survey fJ'r the press service, MSA determines that it must fulfill several requirements inJorder to draw statistically valid conclusions on the. sensitive issue of new US immigration laws: survey at least 2300 US households in tolal survey at leas.L1000 households whose heads are 30 years of age or younger survey at least 600 hOuseholds whose heads are between 31 and 5IJ years of age ensure that at least 15% of those surveyed live in a state that borders on MEXICO ensure that no more than 20% of those surveyed who are 51 years of age or over live in a state that borders on MEXICO MSA decides that all surileys should be conducted in person. it estimates that the costs of reaching people in each age and region category are as' follows " ' COST PER .PERSON SURVEYED($) AGE ::;-3o- AGE 31-50 AGE > 51 STATE 80RDERING MEXICO $7 .50 $6.80 $5.50 STATE NOT BOROERING MEXICO $6.90 $7.25 $6.10 M5A's goal is to meet the 5 sampling requirements at the least possible coSt. MANUFACTURING APPLICATIONS 3_ FIFTH AVE. industries ,a nationally known manufacturer of menswear, produces'four varieties of ties. One is an expensive, all-silk tie, one is an all-polyester tie, .nd two are blends of polyester and cotton. The following table illustrates the cost and availability (per monthly production planning period) of the three materials used in the production process: " 1 / MATERIAL COST PER METER($) MATERIAL AVAIL ABLE PER MONTH (METE R) S ilk 21 800 Polye ster 6 3000 Cotton 9 1600 The firm has fixed contracts with several major department store chains to supply ti es. The contracts require that FIFTH AVE. Industries supply a minimum quantity of each tie but allow for a larger demand if FIFTH AVE chooses to meet that demand.{most of the ties are not shipped with the name FIFTH AVE on their label, incidentally, but with "private stock" labels supplied by the stores. The table below summarizes the contract demand for each of the 4 styles of ties, the selling price per tie, and the fabric: requirements of each variety. FIFTH AV. E's goal is to maximize its monthly profit. It must decide upon a policy for product mix. VARIETY OF SELLING PRICE MONTHLY MONTHLY MATHnAL MATERIAL TIE PER TIE{S) CONTRACT DEMAND REQUIRED , REQUIREMENTS MINIMUM PER llE 1M) All silk 6.70 6000 7000 0.125 '100% silk . All polyester 3.55 10000 14000 . . 0.08 100% polyester . Poly-cotton 4.31 13000 16000 0 .10 50% polyester: blend I 50% cotton Poly - cotton 4.81 6000 8500 0.10 30% polyester- blend II 70% cotton 4_ Gree09!!rg Motors manufacturenwo different electrical motors for sale under contract to Drexel Corp., a well- known producer of small kitchen appliances. Its model GM3A is found in many Drexel food processors and its model GM3B is used in the assembly of blenders, Three times each year, the procurement officer at Drexel contracts Irwin Greenberg, rh'e founder-of Greenberg Motors, to place a monthly order for each of the coming fbur months .. Drexel"s demand for motors varies each month based on its own sales forecasts, production capacity; and financial position. Greenberg has just received the January·Aprii order and must begin his own four-'month production ~ The demand for motors is shown below. Production planning at Greenberg Motors must consider four factors: the desirability of producing the same number of each niotor each month. This simplifies planning and the >cheduling of workers and machines. The necessity to keep down inventory carrying, or holding, costs. This suggests prodUCing in each month only what is needed in that month W'areh'ouse limitations that cannot be exceeded without great additional storage costs · The company's no -layoff policy, which has been effective in prevftlting a unionization of the shop. This suggests a minimum production capacity that should be used each month Although these four factors often conflict, Greenberg has found that LP is an effective tool in setting up a production schedule that will minimize his total costs of per unit production and monthly holding. The production costs currently S10 per GM3A motor produced and $6 pel'GM3B unit. A labour agreement going into effect on March 1 will raise each figure 10%, however. Each GM3A motor held in stock costs $0.18 per month, and each MG3B has a carrying cost of $0.13 per month. Suppose that there are no old motors in stock on January 1. Greenberg also wants to have on hand an additional 450 GM3As and 300 GM3Bs at the end of April. 2 The storage area for Greenberg Motors can hold a maximum of 3300 motors of either type( they are similar in size) at anyone time No worker is ever laid off, Greenberg has a base (at least, minimum) employment level of 2240 labor hours per month. In a busy period, the company can bring two skilled former"employees on board (they are now retired) to increase capacity to (maximum) 2560 hours per month. Each GM3A motor produced requires r.3 hours of labor, and each GM3B takes a worker 0.9 hour to assemble. Table Four Month - order Schedule MODEL JANUARY FEBRUARY MARCH APRIL GM3A 800 700 1000 1100 GM3B 1000 1200 14e6- - N 'Oo-- EMPLOYEE'SCHEDULING APPLICATION 5_ The law firm of IVAN maintains a large staff of young attorneys who hold the title of junior partner. IVAN concerned with the effective utiliz. ation of his personnel resources, s'eeks Someobjective means of making , .Iawyer- to - client assignmerfts~ , On March 1, four new clie~ts seeking lega'i assistance came to IVAN. Although the,current staff i; o~erloaded, IVAN would like to accommodate the ne'w clients. He reviews current case loads and identifies four junior partners who, although busy, could possible be assigned to the cases. Each young lawyer can handle at most one new client. Furthermore, each lawyer differs in skills and specialty interests- , Seeking to maximize the overall effectiveness of the new client assignments. IVAN draws up the following table, in which he rates the estimated effectiveness (on a scale of 1 to 9) oi each bwver on each new case. CLIENT'S CASE LAWYER CORPORATE DIVORCE MERGER EMBEZZLEMENT EXHrBlTIDNISM ADAMS 6 2 8 5 BROOKS 9 3 5 8 CARTER 4 8 3 4 DARWIN 6 7 6 4 Labor Planning 6_ Hong Kong Bank of Commerce and Industry is a busy bank that has requirements for between 1.0 and 18 tellers, depending on the time of day. The lunch time, from noon to 2 P.M .• is usually heaviest. The table below indicates the worker needed at various hours that the bank is open. The bank now employs 12 full-time tellers; but many people are on its roster of available part -time employees. A part - time employee must put in exactly 4 hours per day but can start anytime between 9AM and 1 PM. Part-timers are a fairly inexpensive labor pool, since no retirement or luch benefits are provided for them. Full timers, on the other hand, work from 9 AM to 5 PM but are allowed 1 hour for lunch. Half of the full-timers eat at 11 AM , the other half at noon. Full- timers thus provide 35 hours per week of productive labor time 3 -, TJME PERIOD NUMBER OF TELLERS REQUIRED 9AM-lOAM 10 10AM-llAM 12 llAM-NOON 14 NOON- 1PM 16 1PM-2PM 18 2PM-3PM 17 3PM-4PM 15 4PM -SPM 10 • - By-cerpe Ghicago ~ -- . - __ _ Philadelphia Buffalo 0etroit ~ ________________________________________ ~~~tLo~ ~~~------------------- INGREDIENT BLENDING APPLICATIONS 11_ The whole Food Nutrition center uses three bulk grains to blend a natural cereal that it sells by the pounds . The store advertises that each 2-ounce serving of the cereal when taken with y, cup of whole milk , meets an average adult's minimum daily requirement for protein, riboflavin, phosp'-us, and magnesium units per pound of each are shown in the table below 5 GRAIN CO S T PER POUND PROTEIN RISO FLAVIN PHOSPHORUS M AGNESIUM (CE NT) (UNITS/LS) (UNIT / LS) (UNIT/ LS) (UNIT/ LS) A 33 22 16 8 5 B 47 28 14 7 0 C 38 21 25 9 6 The minimum adult daily requ irement for protein is 3 uni ts,for robiflavin 2 units, for phosphorus 1 unit, for magnezium 0.425 unit. Whole Food wants to select the bl end of grains that will meet the daly requirements at a minimum cost. 12_ the Low Knock Oil company produces two grades of cut-rate ga soline for industrial distribution. The grades, regular and economy, are produces by refining a blend of two types of crude oil, type X100 and type X220. Each crude oil differs no\only in cost per barrel, but-ifl-C-<:lmposition a5 well. The foliowingJable indicates the percentage of crucial ingredients found in each of the crude oils and the cost per barrel for each: CRUDE OIL TYPE INGREDIENT A (%) INGREDIENT B (%) COST/BARREL ($) X100 35 55 30.00 X220 60 25 34.80 Weekly demand fo~ the regular grade of Low Knock gasoline is at least 25000 barrels and demand .for the ecoJlomy is at least 32000 barrels p"er-week. At lea st 45% of each barrel of regular must be ingredient A.·At most . 50 % of each barrel of economy should contain ingredient B . The Low Knock management must decide how many barrels of each type of crude oil to buy each w ee k for blending to satisfy demand at minimum cost. 6