Q$2\text{'}.$ Solve the following LPP by graphical method.

Minimize $Z=20x_1+10x_2$

Subject $to,x_1+2x_{2}40$

$3x_1+x_{2}30$

$4x_1+3x_{2}60$

$x_1,x_{2}0$

Q$3.$ Elaborate the steps involved in finding a solution using the Hungarian method. OR

$(15$ Marks$)$

Q$3\text{'}.$ Find the initial basic feasible solution for the following transportation problenh using VAM.

$\backslash$table$[[$Destination$],[$Origin$,,D_1,D_2,D_3,D_4,$Supply,$],[O_1,11,13,17,14,250,],[O_2,16,18,14,10,300,],[O_3,21,24,13,10,400,],[$Demand$,200,225,275,250,950,]]$

Q$4.$ Explain the need of project management. Discuss the prerequisites for a successful project management. OR

$(15$ Marks$)$

Q$4\text{'}.$ Draw the project network and find the probability that the project is completed in $40$ days.

$\backslash$table$[[$Job$,1-2,1-6,2-3,2-4,3-5,4-5,6-7,5-8,7-8$