Question

(a) A retail chain has 3 distribution centers to serve 4 regions to meet the demand. The transportation cost between the distribution centers and the regions is given in the following table. Unit Transportation Cost for Regions 2 3 4 1 А 12 15 13 11 Distribution B 8 16 12 10 Center C 9 17 11 13 The demand is expected to be 100, 90, 110, and 120 units in regions 1, 2, 3, and 4 respectively. The distribution centers A, B, and C have shipping capacity of 150, 140, 130 units respectively. i. Construct the transportation table for this problem and initialize this problem using the Northwest corner method. (5 pts) ii. What is the total cost for the initial solution? Is the initial solution optimal? (3 pts) iii. If your answer in part ii is YES, explain WHY? If your answer in part ii is NO, apply one iteration of the transportation simplex method and check whether the resulting solution is optimal or not. (7 pts)

Answer 1

دن اوک subbly 2 3 4 15 13. 11: 1o 12 А 12 B 8 9 Demand loo 150 140 130 16 1.7. 11 13 C 90 110 120 3 2 3 4 150 A 100(12) 5015) 13 11 B 40016) 100/12) lo 140 с 9 11 to(11) 120113) 13'0' tvo 90 110 120 ui () TW Total Transportation cost to this Es. 100 X12 + 50 15 + 40 X 16 + 100% 12 + 1oxil + 120 X13 1200 + 750 + 640+1200 + 110.+ 1560 = 5460 Hit This Initial solution is not optimal. obtimality Test: 142) N3) (11) f) (2) (-2) ka ) (13) (16 (12) |(10) (14) +] (5) 19) (12) 19 (15) (9) (13) (-3) (-2) 13 13 119 Too 50 40 (4) 6 120 1) 12 15 since dij are nagetiues therefore this Inutul solution is not optimal

Joo-o SO+9 40-ө (об о ( Sime minimum allocation contuning -9 is 40-1 от 40 Taking 40-050 le ut' (12) (0) б бо (0) (3) (16) m) Чо (3) (16) (у Ф) 10) Тоб (1) (8) чо – Ч. S) (4) (13) а) 7 +) (10) То Іго (2) (7) 18 12 15 y ар 50-6 9o . його Job - 16+0 Т%-0 Since minimum-allocation contains ao es и во-19 * таһу во-ове квесь

45 " (12) G) Is) |(3) ७)) १० 60 ) |(8) (16) (18) (1) (10) 100 40 () (9) (1)/07) (2) D (13) 70 to (2) (0) 3 ॐ '2 S । १ m j १० 60 100 ५०० A 10+860-8 Takery ५०-6 20, 8:40 us (13) I) () TCS) १० (3) Go 0 (6) (1५) (12) (8010) 40 100 (२) १) (01) (ए) 1) (5) 2 110 20 (2) b 5. ॥ १ IS १ d31 E-250 therefore solution is not optimal in-dostikkudnepal

. % Go 100 yotol 0 llo Takery 86-00 0=20 ul |(12) 163) fur ) (15) 90 bo (3) (2) (16) 14)|(2) 80 bo (2) 19) (9) KOO (15) (11) 110 (29 15 al !! १ 11 woj since all dij so therefore the solution is optimal.. and is given by. 842=90 243.760, 31-80: 223560 2317 20 233-110 optimal cost = 15x90 + 11 60 + 8%-80 +10x60 + 9x20 +11 Xllo = 1350 of 660 & 640 600 +180 + 1210 1 4640 Ant