Question

how to solve using goal programming and deviational variables

(b) Solve the following goal programming model graphically. Minimize Pdf + Pdy + Pad + Pgda Subject to 4X1 + 8X2 + dī - d = 45 8X1 + 24X2 + d - d = 100 X1 + 2X2 + d3 - dj = 10 X1 + dī - dt = 6 (c) Repeat the above problem with the objective to minimize Pidi + P2dz + P3d + P3dī

Answer 1

(6) Solve graphically Minimize 2 = dit + 12 de + 2 + 3y St. 4x + 8x₂ + di- dit = us d (11.25,0), (0.5.625) 8x + 24x + dy - dat = 100 (12.5, 0), (0, 4.167) X1 + 2x2 + do- d = 10 - (10,0), cos 1 t dir-dut = b = (60) dj, dj increases if the direction ( ) 10,5.625) .P(5, 2.5) 1671 . first prissity is , dgt we have to min dit so opposite asen will be feasible for at second dat opposite an would be feasible because in this side it will be zero. Third priority is Pz dz t + Pz du first is dyt so we satisfy it first so area would be (6,5), (o 4.167/ and P (525) so it point is (0,5) then d = 5 det = 20 and du = 6 then min = 6

optima point of Point (0) 4.167) is if entome point on 4.167) is point then di = 11.67, di = 1.17, du then min z = 6 of Point is (5,2.5) then d = 1 then min 7 = 1 ond, =S, 14 = 1 (5, 25) is optimal becasse min 6, 6, 1) = 1 for this & point n = 5 M = 2.5 Now if z= P, di +82 d 2 + P2 det +Pudy then 18-dyt (12.5°)

get feasible are is lighlighted part so feasible points are o, 5.625), (6, 2/2) ( 35, 5), (1215,0) Extreme Points Min z (o, 5.625 1.25 (6, 2.625) 1.25 (8.75 1.25 ) 1.25 (12.5, 0) 2.5 three optimal points corresponding So to here we have min z = 1.25.