Question

Use the method of this section to solve the linear programming problem.

Maximize	P = x − 3y + z
subject to	2x + 3y + 2z ≤ 4 x + 2y − 3z ≥ 2 x ≥ 0, y ≥ 0, z ≥ 0

The maximum is P =  

at (x, y, z) = .

Answer 1

06 - the + L 2x+ 2 > risustly to, obol.) Given, Maximize Pa Subject to 3y + qz cu x + ay - 32 > 2 83,01 y so, 27/0 conveut into we 'I' by multiply both sides, then we get Maximize Po x-3y + 2 Subject 2x + 3y + 92 24 - 30 2010, Now. converting the inequalities to equa by introduction of stack variables, 2x + 3y + 22 t u - 3 + 2y + 32 + u -2 Taking then, 4 g Now, constructing the simplex tablet Mini 0 Все | Xe | x XB/XC u g Key 3 u + mini +32 L-Q y >0, >0 h: X = 0, yao X=0 U- Ci 1 0 Ratio L u ७ y 6 น elemért ७ ol-2 I -2 3 O a Z= CB X Blog -3 1 - 0 0

oc Incoming vector Outgoing element vector u ee key C -3 O 0 Minu Ratiol Xol B CB X₂ x L ܫ u ७ 8 g 312 est O o -Yg 4 [alg ya -ya g O 9 10 Z=CB XB Djo Since all the Dj's for non- basic variables che negative So this solution is optimd. Optimal soln is. yo 1 x = 0 and mascimum is psg X g