IFoS PYQs 3
2007
1) Solve the following LPP by graphical method: Maximize \(Z=5 x_{1}+7 x_{2}\) subject to \(x_{1}+x_{2} \leq 4\) \(3 x_{1}+8 x_{2} \leq 24\) \(10 x_{1}+7 x_{2} \leq 35\) \(x_{1}, x_{2} \geq 0\)
[10M]
2) Solve the following LPP by simplex method: Maximize \(Z=2 x_{1}+5 x_{2}+7 x_{3}\) Subject to \(\begin{array}{r} 3 x_{1}+2 x_{2}+4 x_{3} \leq 100 \\ x_{1}+4 x_{2}+2 x_{3} \leq 100 \\ x_{1}+x_{2}+3 x_{3} \leq 100 \\ x_{1}, x_{2}, x_{3}\geq0 \end{array}\)
[10M]
3) Solve the following minimal assignment problem:
| \(Man\to\) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \(I\) | 12 | 30 | 21 | 15 |
| \(II\) | 18 | 33 | 9 | 31 |
| \(III\) | 44 | 25 | 24 | 21 |
| \(IV\) | 23 | 30 | 28 | 14 |
[10M]
2006
1) Find the basic feasible solutions of the following system of equations in a linear programming problem \(\begin{array}{l} x_{1}+2 x_{2}+x_{3}=4 \\ 2 x_{1}+x_{2}+5 x_{3}=5 \end{array}\)
[10M]
2) TBC Use Simplex method to solve the following linear programming problem Maximize \(Z: 2 x_{1}-x_{2}+3 x_{3}\) subject to constraints \(3 x_{1}+x_{2}-2 x_{3} \leq 6\) \(2 x_{1}+5 x_{2}+x_{3} \leq 14\) \(x_{1}+4 x_{2}+2 x_{3} \leq 8\) \(x_{1}, x_{2}, x_{1} \quad \geq 0\)
[10M]
2005
1) Find the basic feasible solutions of the following system of equations in a linear programming problem \(x_{1}+2 x_{2}+x_{3}=4 2 x_{1}+x_{2}+5 x_{3}=5\) \(x_{1} \geq 0, j=1,2,3\)
[10M]
2) Solve the linear programming problem Find \(mm \left(8 x _{1}+6 x _{2}\right)\) subject to the constraints \(4 x_{1}+3 x_{2} \geq 18\) \(2 x_{1}+5 x_{2} \geq 16\) \(x_{1}, x_{2} \geq 0\) using graphical method. Show that more than one feasible solvtion will yield the minimum of the objective function. Interpret this fact geometrically
[10M]
3) Use simplex method to solve the following linear programming problem. Maximize \(Z=2 x_{1}=x_{2}+3 x_{3}\) subject to the constraints. \(3 x_{1}+x_{2}-2 x_{3} \leq 6\) \(2 x_{1}+5 x_{2}+x_{3} \leq 14\) \(x_{1}+4 x_{2}+2 x_{3} \leq 8\) \(x _{1+} x _{2}, x _{3} \geq 0\)
[10M]