2008

2007

1) Solve the following LPP by graphical method: Maximize $Z=5x_1+7x_2$ subject to $x_1+x_2\le 4$ $3x_1+8x_2\le 24$ $10x_1+7x_2\le 35$ $x_1,x_2\ge 0$

[10M]

2) Solve the following LPP by simplex method: Maximize $Z=2x_1+5x_2+7x_3$ Subject to $\begin{array}{r}3x_1+2x_2+4x_3\le 100\\ x_1+4x_2+2x_3\le 100\\ x_1+x_2+3x_3\le 100\\ x_1,x_2,x_3\ge 0\end{array}$

[10M]

3) Solve the following minimal assignment problem:

[10M]

2006

1) Find the basic feasible solutions of the following system of equations in a linear programming problem $\begin{array}{l}{x}_1+2x_2+x_3=4\\ 2x_1+x_2+5x_3=5\end{array}$

[10M]

2) TBC Use Simplex method to solve the following linear programming problem Maximize $Z:2x_1-x_2+3x_3$ subject to constraints $3x_1+x_2-2x_3\le 6$ $2x_1+5x_2+x_3\le 14$ $x_1+4x_2+2x_3\le 8$ $x_1,x_2,x_1\ge 0$

[10M]

2005

1) Find the basic feasible solutions of the following system of equations in a linear programming problem $x_1+2x_2+x_3=42x_1+x_2+5x_3=5$ $x_1\ge 0,j=1,2,3$

[10M]

2) Solve the linear programming problem Find $mm(8x_1+6x_2)$ subject to the constraints $4x_1+3x_2\ge 18$ $2x_1+5x_2\ge 16$ $x_1,x_2\ge 0$ 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 $Z=2x_1=x_2+3x_3$ subject to the constraints. $3x_1+x_2-2x_3\le 6$ $2x_1+5x_2+x_3\le 14$ $x_1+4x_2+2x_3\le 8$ $x_{1+}{x}_2,x_3\ge 0$

[10M]