Critical Path Method $($CPM$)$ Class Exercise: Draw the path diagram, identify the critical path, and find the optimal solution in days and the final cost of the project. Indirect costs are $$200$ per day and a penalty cost of $$100$ is incurred on day $13$ and every day after of $$100.$ Show all work.

$\backslash$table$[[,\backslash$table$[[$Immediate$],[$Predecessor$]],\backslash$table$[[$Normal$],[$time$]],\backslash$table$[[$Crash$],[$time$]],\backslash$table$[[$Normal$],[$cost$]],\backslash$table$[[$Crash$],[$cost$]],\backslash$table$[[$Maximum$],[$Reduced time$]],\backslash$table$[[$Crashing$],[$cost$/$day$]]],[$A$,$dots$-,4,3,1,000,1,300,1,\frac{30}{\frac{?}{?}}=300$