A shop floor performs $3$ different operations on a part. Operation $1,2$ and $3$ takes $4,7$ and $5$ minutes respectively to complete. The raw material is arriving with exponential distribution of $(0,5,0)$ minutes. There is manual handling $($operator travel speed $5$m$/$min$)$ of parts up to completion of all the operations. After which, a forklift $($speed $20$ m$/$min$)$ carries bunch of $5$ parts to the shipping point. Find,

$1.$Throughput of shop floor. $($Run time: see from the sheet provided on elearn portal$).$

$2.$ Find Utilization of resources.

$3.$ Suggestions for optimizing the shop floor