Consider the product mix problem summarized in the table with $3$ products $($A$,$ B$,$ and C$)$ and $5$ types of resources $(1,2,3,4,5).$ There may be multiple workers working in parallel for each resource. Assume that all workers have $8$ hours per day. The number of workers in each resource and the times required for each activity $($product$)$ in each resource are given in Table $1.$

Table $1$ process times for sub products$$Work stations$$Number of workers$$Activity time for A $($Min$/$Unit$)$Activity time for B $($Min$/$Unit$)$Activity time for C $($Min$/$Unit$)15555243453415004604358101010$

Assume that the activity times given in Table $1$ are for experienced workers and the time requirements are $\%50$ more for inexperienced workers. Also, assume that our workforce is composed of $12$ experienced and $15$ inexperienced workers that can be assigned to any workstation. Formulate and solve a linear program $($with your favorite mathematical solver$)$ to find the optimal workforce assignment to workstations to maximize the flow rate.