(based on simplex method, charne’s big m method) · solve the following l.p.p. by big m-method :...
TRANSCRIPT
ASSIGNMENT 2(Based on Simplex Method, Charne’s Big M Method)
Q.1. Solve the L.P.P.Maximize z = 5x1 + 2x2 + 2x3
subject to x1 + 2x2 − 2x3 ≤ 30
x1 + 3x2 + x3 ≤ 36
x1, x2, x3 ≥ 0.
(a) zmax = 150 (b) zmax = 174 (c) zmax = 188 (d) zmax = 65
Q.2. Solve the following L.P.P. by simplex method :
Minimize z = −3x1 + 2x2
subject to x1 − 4x2 ≤ −14
−3x1 + 2x2 ≤ 6
x1, x2 ≥ 0.
(a) zmin = 6 (b) zmin = -13 (c) No feasible solution (d) Unbounded Solution
Q.3. Solve the following L.P.P. by Big M-method :
Maximize z = 5x1 + 11x2
subject to 2x1 + x2 ≤ 4
3x1 + 4x2 ≥ 24
2x1 − 3x2 ≥ 6
x1, x2 ≥ 0.
(a) zmax = 10 (b) zmax = 25 (c) No feasible solution (d) Unbounded Solution
Q.4. Use simplex method to solve the following L.P.P.
Maximize z = 5x1 + 2x2
subject to 6x1 + 10x2 ≤ 30
10x1 + 4x2 ≤ 20
x1, x2 ≥ 0.
1
Is the solution unique?
(a) zmax = 10. Unique (b) zmax = 10. Not unique (c) zmax = 25. Unique(d) zmax = 25. Not unique
Q.5. Use the simplex method to solve the L.P.P.
Maximize z = 2x2 + x3
subject to x1 + x2 − 2x3 ≤ 7
−3x1 + x2 + 2x3 ≤ 3
x1, x2, x3 ≥ 0.
(a) zmax = 12 (b) zmax = 6 (c) No feasible solution (d) Unbounded solution
Q.6. Solve the L.P.P. by simplex method
Minimize z = x1 − 3x2 + 2x3
subject to 3x1 − x2 + 2x3 ≤ 7
−2x1 + 4x2 ≤ 12
−4x1 + 3x2 + 8x3 ≤ 10
x1, x2, x3 ≥ 0.
(a) zmin = -11 (b) zmin = -9 (c) No feasible solution (d) Unbounded solution
Q.7. Find xj ≥ 0, (j = 1, 2, 3, 4)
subject to x1 + 2x2 + 3x3 = 15
2x1 + x2 + 5x3 = 20
x1 + 2x2 + x3 + x4 = 10
which will maximize the functionx1 + 2x2 + 3x3 − x4.
(a) No feasible solution (b) Unbounded solution (c) zmax =90
7(d) zmax = 15
Q.8. Solve the following L.P.P. with the help of simplex method :
Maximize z = 4x1 + 14x2
2
subject to 2x1 + 7x2 ≤ 21
7x1 + 2x2 ≤ 21
x1, x2 ≥ 0.
(a) No feasible solution (b) Unbounded solution (c) zmax = 42 (d) zmax = 0
3
ANSWERS
Q.1. (b)
Q.2. (d)
Q.3. (c)
Q.4. (b)
Q.5. (d)
Q.6. (a)
Q.7. (d)
Q.8. (c)
4
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner