Using the closed network of queues model, analyze the following problem. A job shop has three machines. Four products are made according to Table $11\mathrm{.}7.$ One material handler is available, and it takes him about $5$ minutes to move a load of material between machines. You may assume that the handler is not needed to deposit new parts to the first operation. Machines $1$ and $2$ run $40$ hours per week, and machine $3$ runs $80$ hours. Assume that we try to keep one week$$s demand worth of work in process at all times.

$1.$Analyze by explicitly modeling the four separate products.

$2.$Aggregate the four products into a generic $($weighted$-$average$)3.$Re$-$solve problem $11\mathrm{.}19$b as an open network. Arrival rates are given by weekly demand. In addition to finding average throughput time for an arbitrary job, find the average throughput time for product type $1$ specifically. product and reanalyze. $3.$