Develop a simulated annealing procedure in either R or Python to solve the same knapsack problem: $($Note$,$ this problem can be solved to optimality using integer programming; however, the focus of this question is on developing the simulated annealing method$).$ Do not simply return a shell code from a web search, but try to implement the simulated annealing metaheuristic for this specific problem.

Maximize $12$x$1+16$x$2+22$x$3+8$x$4$

S$.$T$.4$x$1+5$x$2+7$x$3+3$x$4<=140$

$0<=$ xi $<=10$ and xi is integer