GATE 2023 MA – Question 57
For a balanced transportation problem with destinations P,Q,R,S, the five cost rows and supplies are: source 1:(13,8,12,9),20; source 2:(10,7,5,20),10; source 3:(3,19,5,12),50; source 4:(4,9,7,15),30; source 5:(14,0,1,7),40. Destination demands are (60,10,20,60). Let C_N,C_L be initial basic feasible costs from the North-West corner and Least-Cost methods. Find C_N−C_L.
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Correct answer: 380 to 380
Explanation
North-West allocations are (1P,2P,3P,3Q,3R,4R,4S,5S)=(20,10,30,10,10,10,20,40). Cost=260+100+90+190+50+70+300+280=1340. Least-Cost allocations are 5Q=10,5R=20,3P=50,4P=10,5S=10,1S=20,4S=20,2S=10. Their cost is 0+20+150+40+70+180+300+200=960. Difference=**380**.