GATE 2023 MN – Question 57
Three mines supply four washeries. Unit transportation costs for (W1, W2, W3, W4) are M1:(19, 30, 50, 10), M2:(70, 30, 40, 60), M3:(40, 8, 70, 20). Supplies are (700, 900, 1800) tonnes/day; demands are (500, 800, 700, 1400). Find the initial basic feasible solution cost using Vogel’s approximation method, to one decimal.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 77900 to 77900
Explanation
Compute row/column penalties as the difference between the two cheapest available costs. The first allocation is M3→W2:800 (largest penalty 22), then M1→W1:500 (penalty 21), then M3→W4:1000 (penalty 30). Allocate the remaining M1 supply 200 to W4, leaving M2→W4:200 and M2→W3:700. Cost = 800×8+500×19+1000×20+200×10+200×60+700×40 = 77900.0. Supplies and demands both total 3400, so no dummy source is needed.