Quantitative techniques

(a) The Garlin Textile Group which has three factories in Mauritius distributes linen and other fabrics to three leading retail stores across the island. The factory availabilities, projected store demands and unit shipping costs are summarized in the given table. Using Vogel's approximation method, determine the initial solution to this transportation problem. Use Modi's method to determine an optimal transportation solution. Transportation costs from factory to store To STORE Factory From A B C Capacity F1 10 7 8 45 F2 15 12 9 15 F3 7 8 12 40 DEMAND 25 55 20 (b) A manager has four supervisors and four tasks to be performed. The supervisors differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the times (in minutes) each supervisor would take to perform each task are given in the matrix below: TASKS A B C D Supervisors 1 7 3 4 5 W N 5 4 6 7 6 7 9 8 4 8 6 5 How should the tasks be allocated to the supervisors so as to minimize the total time