Problem $2$: Consider a process that produces flow units of Products x and y: Activities: A$1,$ A$2,$ A$3,$ A$4,$ Resources: r$1,$ r$2,$ r$3,$ r$4,1$ unit each. Product x goes through A$1,$ A$2,$ and A$3$; Product y goes through A$1$ and A$4.$ Among all the flow units that go through the process, $30\%$ are Product x and $70\%$ are Product y$.$Draw the collaboration graph of this process and tell whether the bottleneck formula can be used to compute the capacity.$($b$)$ Use the bottleneck formula to compute capacity regardless of whether or not it can find the real capacity.$($c$)$ Find an LP formulation for calculating the capacity of this process.