a$.$ Solve the following Linear Programming problem and obtain optimum solution. $($X$1,$ X$2,$ X$3,$ X$4,$ X$5>=0)$

b$.$ You have been informed that X$1$ is a binary variable and X$2$ is an integer variable.

Now, solve this mix integer programming problem and obtain optimum solution. $($X$1-$ binary, X$2-$ integer, X$3,$ X$4,$ X$5>=0)$

Profit per unit $569810$

X$1$ X$2$ X$3$ X$4$ X$5$

Constraint $1136<=10000$

Constraint $25161<=12000$

Constraint $361<=20000$

Constraint $41611<=50000$