QUESTION ONE (a) Differentiate between an assignment problem and a transportation problem. (2 Marks) (b) Maris Ltd. Co has five types of machines, V, W, X, Y and Z to be assigned to five jobs namely; A, B, C, D and E on the basis of one and only one. The table below shows the amount of hours that each machine would take to do each job. The company wants to minimize the number of hours the machine will be used to do the job assigned. Machine Job A B C D E V 20 15 18 20 25 W 18 20 12 14 15 X 21 23 25 27 25 Y 17 18 21 23 20 Z 18 18 16 19 20 Required: Using the Hungarian method, determine the companys optimal assignment. (8 Marks) (c) The distribution system of Jones Ltd Co. has the following constraints. Factory Capacity (in units) M 100, 000 N 40, 000 O 90, 000 @milkah pg. 2 Warehouse Capacity (in units) 1 60, 000 2 120, 000 3 50, 000 The transportation cost per unit (in Shillings) from each factory to every warehouse is given in the table below. From factory To Warehouse 1 2 3 M 30 24 26 N 40 34 28 O 24 26 34 Required: (10 Marks) You must check for optimality in each case using Modified distribution method. a) Using the NWCM, determine the initial transportation cost hence the optimal solution. b) Using the LCCM, determine the initial transportation cost hence the optimal solution. c) Using the VAM, determine the initial transportation cost hence the optimal solution.