Question: QUESTION THREE (a) What is the shortest-path problem? Give some practical applications of the shortest- path problem (3 Marks) Page 3 of 5 (b) Giving

QUESTION THREE (a) What is the shortest-path

QUESTION THREE (a) What is the shortest-path problem? Give some practical applications of the shortest- path problem (3 Marks) Page 3 of 5 (b) Giving suitable examples, what are the types of transportation problem? (3 Marks) (c) Consider the transportation problem shown in Figure 1: supply 1 2 3 2 4 5 1 2 3 7 3 3 8 7 5 1 7 2 4 4 1 6 14 Demand 2 9 18 Figure 1: Solve the problem using Northwest corner cell method (5 Marks) (i) Write the procedure you would take to optimize your solution from (1) (2 Marks) (d) Consider company Z that wants to transport goods from 4 sources to 2 destinations in Lusaka. The sources and destinations can be used as transient nodes forming a transshipment problem. The supply values of the sources Si, S2, Ss and Se are 200 units, 250 units, 200 units and 450 units, respectively. The demand values of the des- tinations D, and D, are 550 units and 550 units, respectively. The transportation cost per unit between different sources and destinations are summarized in Figure 2: Solve the transshipment problem such that the total cost of transportation is mini- mized. Hint: Use VAM Method. (7 Marks) () Draw a diagram showing the directions that should be taken from each source to each destination via transient nodes. (3 Marks) (i) What is the value of the objective function? (2 Marks) [TOTAL: 25 Marks] Page 4 of 5 cesmanon DESTINATION 51 52 D1 02 all 51 0 7 24 10 53 10 0 12 5 20 55 15 20 7 SOURCE 54 30 6 DI 15 20 60 15 0 10 23 0 Figure 2: QUESTION THREE (a) What is the shortest-path problem? Give some practical applications of the shortest- path problem (3 Marks) Page 3 of 5 (b) Giving suitable examples, what are the types of transportation problem? (3 Marks) (c) Consider the transportation problem shown in Figure 1: supply 1 2 3 2 4 5 1 2 3 7 3 3 8 7 5 1 7 2 4 4 1 6 14 Demand 2 9 18 Figure 1: Solve the problem using Northwest corner cell method (5 Marks) (i) Write the procedure you would take to optimize your solution from (1) (2 Marks) (d) Consider company Z that wants to transport goods from 4 sources to 2 destinations in Lusaka. The sources and destinations can be used as transient nodes forming a transshipment problem. The supply values of the sources Si, S2, Ss and Se are 200 units, 250 units, 200 units and 450 units, respectively. The demand values of the des- tinations D, and D, are 550 units and 550 units, respectively. The transportation cost per unit between different sources and destinations are summarized in Figure 2: Solve the transshipment problem such that the total cost of transportation is mini- mized. Hint: Use VAM Method. (7 Marks) () Draw a diagram showing the directions that should be taken from each source to each destination via transient nodes. (3 Marks) (i) What is the value of the objective function? (2 Marks) [TOTAL: 25 Marks] Page 4 of 5 cesmanon DESTINATION 51 52 D1 02 all 51 0 7 24 10 53 10 0 12 5 20 55 15 20 7 SOURCE 54 30 6 DI 15 20 60 15 0 10 23 0 Figure 2

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