Question

Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).

Answer 1

ANSWER:
Gy even that; Subject to Men zs 3x1-x2 224 +2 28 4 + X2 25 XI-X2 24 nugol 2 zo sleek s Swreples a) The problem is converted to standard frou by adding pleee and are té fece al Narceables as appropriate :- ) As the constraint -1 s of type s' we should add slack Variable si id) As the constraint -2 or of type 't we should add slack variable el. 200) the constreownt - s us of type 'L' we should add slack variable sa Aftere in treodecong slaik vare'oblee:- Monz - 34 - R2 tosit oft Of subject to pri tx2+8, 422 th=5 4.42 tsg=y and X2 is S21S3.70 58 3

2 b) step Itercatio of fable: Iteration 1 ej 3 -1 6 0 0 B CB X2 X1 сол 82. S3 Mon Rate o XB X2 81 2 1 1 2 $2. 15 را) - 0 & ES → o S3 0 4 1 0 1 0 0 1 zo 0 0 0 Zj Zj-cj O In -3 o inden po se teve Make your z; rcj 1 and Ets coleen Era . so, the entering variable of X2 Money am 'reatio ex 5 and i te reow Endex 2. 80s the leeveng basele vereable cope 32 " The pivot element && 1. Egtering = X2 Departong key elemental Step-2 Be (new) = R2 cold) and Iteraton R2 cold) 5 R2 (opew I5R2(old) & S2 1 0 11 o - 1 olto

Ricnew) = Ro Cold) - B2 (new) - Rilnew) = 8.2 o 0 R2 (new) 5 lo 0 1 0 1 0 RiCnew ]=- Riloid J. – Bloem) 3 Rs lorew) = R3 (old) + R2 (ew) 0 1 T 1 0 1 Rå (oldfy Ra (new) = 5 Ral new ) = R3lold ) +R2107ew) 9 2 o - 0 Iteration 2 3 0 ī Cj. .XB CB 81 X2 31 (2 23 Men Roteo 3 - 1 0 - Si X2 S3 5 0 0 2 1 - z = 5 9 Z; Zj-ej 1 TIT OO 0 ry 0 since all Z-GLO etion is arrived with value of Hence, Optery of solectio Vareetables as c X1 X2 =5 Min z=5 Ang