1) [3 marks] Four matches, in four different cities, would be held this coming Thursday in the national football league. Five referees, from five different locations, are available to judge the four matches. The distances, in km, that every referee needs to drive to reach each of the four cities are given in the following table. Assign exactly one referee for each match, such that the total distance covered by all referees is minimized. Referee 1 Referee 2 Referee 3 Referee 4 Referee 5 City 1 City 2 City 3 City 4 210 90 180 160 100 70 130 200 175 105 140 170 80 65 105 120 95 115 120 100 2) [7 marks] A company has two factories to fabricate prayer mats in Dammam and Hafr Albatin. The two factories supply 150 and 200 mats per day, respectively. Customers of the company in Makkah and Madinah have a demand of 130 mats per day each. The company believes that it may be cheaper to first ship some mats to Riyadh or Hail then ship them to their final destinations. The costs, in SAR, of shipping one unit are given in the following table. The company wants to minimize the total cost of shipping the required units to its customers. Riyadh 8 15 Dammam Hafr Albatin Riyadh Hail Hail 13 12 6 Makkah 25 Not Possible 16 14 Madinah Not possible 25 17 16 6 a. Draw the network diagram that represents the problem. Clearly put each cost over its corresponding arc. b. Build the transshipment table that represents the problem C. Find the initial feasible solution using the northwest method d. Find the initial feasible solution using the least cost method e. Find the initial feasible solution using the VAM method f. Use the method of multipliers to improve the VAM initial feasible solution, in (e), till you reach the optimum shipping strategy g. Draw the network diagram that represents the optimum strategy, which you get in (1)