$\mathrm{.}1$ A High learning institute is planning a new product line and will build a new plant to manufacture the parts for a new product line. The product line will include $50$ different models. Annual production of each model is expected to be $500$ units. Each product will be made up of $200$ components. All parts will be processed in $1$ factory. There are an average of $6$ processing steps required to produce each component, and each processing step takes $120$ seconds $($includes an allowance for setup time and part handling$).$ All processing operations are performed at workstations, each of which includes a production machine and a human worker. If each workstation requires a floor space of $90$ metres and the factory operates $1$ shift $(2000$ hr$/$yr$.),$ determin