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Quantitative Methods in Administration Problem Set # 5: Transportation and Assignment Problems 1. Reytana Enterprises hauls oranges between Nueva Vizcaya groves and Metro Manila public markets. The enterprise's schedule this week calls for 520 boxes with locations and other information as follows: GROVE AVAILABLE MARKETS REQUIREMENT (BOXES/WEEK) (BOXES/WEEK) 170 Quiapo 130 250 Divisoria 200 100 Muntinlupa 190 The cost information included: (expressed in hundreds of pesos) TO FROM QUIAPO DIVISORIA MUNTINLUPA Grove A 12 Grove B 11 15 agu Grove C 2 Use the MODI method to find the lowest transportation cost. 2. San Miguel Corporation has three warehouses in Calamba City that supply four major supermarkets with cases of beer. Each warehouse has 30 cases of beer. Supermarkets 1, 2, 3 and 4 require 20, 25, 30 and 35 cases of beer, respectively. The per unit shipping costs from each warehouse to each supermarket are: WAREHOUSE SUPERMARKET 1 2 3 4 50 40 60 50 30 60 40 40 WN 40 30 30 20 Required: a) Draw a network representation for this problem. b) Set up the initial transportation table. What is the total shipping cost?3. Coach Christine Jacobs is putting up a relay team for the 400-meter relay. Each swimmer must swim 100 meters of breaststroke, backstroke, butterfly or freestyle. Christine believes that each swimmer will attain the times in the table below. To minimize the team's time for the race, which swimmer should swim which stroke? TIME(seconds) SWIMMER FREE BREAST FLY BACK Ryla Czarina Durante 54 54 51 53 Daphne Joyce Rosales 51 57 52 52 Mae Abigail Oberos 50 53 54 56 Pamela Mae Pullantes 56 54 55 53 4. The Department of Agribusiness Management has decided to apply the Hungarian method in assigning professors to courses next semester. As a criterion to judging who should teach each course, the chairman of the graduate instruction committee reviews the past two years' teaching evaluations which were filled up by students. Since each of the four professors taught each of the four courses at one time or another during the two-year period, she is able to record a course rating for each instructor. These effectiveness ratings are shown below: COURSE PROFESSOR QUANTI MGT 201 PRODUCTION FINANCE Melgar 80 60 89 75 Madamba 90 65 95 80 Tan 85 89 96 61 Williams 67 90 81 93 Find the best assignment of professors to courses to maximize the overall teaching rating