Consider the product mix problem summarized in the table with $3$ products $,$ and $C$ and $5$ types of resources $(1,2,3,4,5).$ There may be multiple workers working in parallel for each resource. Assumte 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

$\backslash$table$[[\backslash$table$[[$Work$],[$stations$]],\backslash$table$[[$Number of$],[$workers$]],\backslash$table$[[$Activity time for A$],[($Min$/$Unit$)]],\backslash$table$[[$Activity time for B$],[($Min$/$Unit$)]],\backslash$table$[[$Activity time for C$],[($Min$/$Unit$)]]],[1,5,5,5,5],[2,4,3,4,5],[3,4,15,0,0],[4,6,0,4,3],[5,8,10,10,10]]$

For the given setting answer the following questions:

a$.$ What is the maximum flow rate if demand must be served in the mix determined by the demand rate $(7$ units of $A,5$ units of $B,$ and $4$ units of $C?$

b$.$ What is the bottleneck workstation,

What is the utitization of workstations?