Assesment $5-$ Problem $1$

a$.$ Solve the following Linear Programming problem and obtain optimum solution. $($X$1,$ X$2,$ X$3,$ X$4>=0)$

b$.$ You have been informed that variables X$3$ and X$4$ are integer variables.

Now, solve this mix integer programming problem and obtain optimum solution. $($X$1,$ X$2>=0,$ X$3,$ X$4-$ integer$)$

MaxZ$=25x1+32x2+36x3+20x4$

Subject to:

$6x1+7x2+4x3+2x4950$

$3x1+4x2+8x3+3x4900$

$7x1+7x2+8x3+9x42000$