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Baó cáo nghiên cứu và áp dụng kiến thức của QUY HOẠCH TUYẾN TÍNH dựa trên lý thuyết được học của môn Phương pháp định lượng và phần mềm QM for Windows. selecting an effective media mix. Sometimes the technique is used for allocating a fixed or limited budget across various media including radio or television commercials, newspaper ads, direct mailings, magazine ads, and so on. In other applications, the objective of the technique is the maximization of reach of audience. Therefore, we decided to create a case study about media selection to acknowledge about LP in marketing application. Obito Mandara is a manager of a hoodie store in Suwon city. Recently, he and marketing team have been planning a campaign to attract customers as well as gain competitive advantages. There are four selected ways to advertise: television ads, facebook ads, google ads, poster ads. The cost of ads, the reach of audience following each type of ad and the maximum number of each ads are shown in the below table: Type of ad Cost per ad Audience reachedad Maximum number TV 1000 35,000 10 Facebook 650 25,000 10 Google 720 30,000 10 Poster 120 9,000 10 Furthermore, they decided that TV or Facebook or come combination of those two should be at least 8ads. The amount spent on Google and Poster must not exceed that on TV ads. Addition, meanwhile looking for funding, 17,000 has been monthly budget for ads. How many ads of each type to maximize the total number of people reached?
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY SCHOOL OF INDUSTRIAL MANAGEMENT _ GROUP ASSIGNMENT COURSE: QUANTITATIVE METHODS CLASS: CC17QKD INSTRUCTOR: PHAM QUOC TRUNG Group members : Ho Chi Minh city - 2019 OBJECTIVES OF THE STUDY The objective of the study is to focus on analyzing and applying the knowledge of linear programming based on the theoretical principles and the practical soft-wares In this study, we decide to choose the case about Obito Mandara (a manager)- to help him select an effective media channel; and Chase Manhattan Bank- to arrange labor forces to minimize the labor cost CASE STUDY Linear programming models have been used in the advertising field as a decision aid in selecting an effective media mix Sometimes the technique is used for allocating a fixed or limited budget across various media including radio or television commercials, newspaper ads, direct mailings, magazine ads, and so on In other applications, the objective of the technique is the maximization of reach of audience Therefore, we decided to create a case study about media selection to acknowledge about LP in marketing application Obito Mandara is a manager of a hoodie store in Suwon city Recently, he and marketing team have been planning a campaign to attract customers as well as gain competitive advantages There are four selected ways to advertise: television ads, facebook ads, google ads, poster ads The cost of ads, the reach of audience following each type of ad and the maximum number of each ads are shown in the below table: Type of ad Cost per ad TV Facebook Google Poster $1000 $650 $720 $120 Audience reached/ad 35,000 25,000 30,000 9,000 Maximum number 10 10 10 10 Furthermore, they decided that TV or Facebook or come combination of those two should be at least 8ads The amount spent on Google and Poster must not exceed that on TV ads Addition, meanwhile looking for funding, $17,000 has been monthly budget for ads How many ads of each type to maximize the total number of people reached? Solution: The very first step is to formulate the problem and define the variables Let: x1: TV ads x2: Facebook ads x3: Google ads x4: Poster ads Objective function: Max: Z= 35,000x1 + 25,000x2 + 30,000x3 + 9,000x4 Constraints: 1000x1 + 650x2 + 720x3 + 120x4 =55 (5) 2-3pm: F+P3+P4+P6+P7+P8+P9+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21>= 60 (6) 3-4pm: F+P4+P7+P8+P10+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22>=51 (7) 4-5pm: F+P8+P11+P12+P13+P14+P15+P16+P17+P18+P19+P20+P21+P22>=29 (8) 5-6pm: (F1+F2) +P12+P15+P16+P17+P20+P21+P22>=14 (9) 6-7pm: (F2) +P16+P19+P21+P22>=9 (10) For the factor 1: By corporate policy, part-time personnel hours are limited to a maximum of 40% of the day’s total requirement Constraint 11: 4(P1+P5+P9+P13+P17+P20+P22) +5(P2+P6+P10+P14+P18+P21)+ 6(P3+P7+P11+P15+P19)+ 7(P4+P8+P12+P16)