The break$-$even point is to be determine for two production methods, one a manual methods and the other automated. The manual method requires four works at R$12$hr each. They produce at a rate of $40$ units$/$hr$.$ the automated method has an initial cost of R$125000,$ a $4$ year service life, no salvage value, and annual maintenance costs $=$ R$4500.$ No labor $($except for maintenance$)$ is required to operate the machine, but the power required to run the machine is $50$ kW $($when running$).$ Cost of electric power is R$0\mathrm{.}05/$kwh$.$ If the production rate for the automated machine is $200$ units$/$hr$.$

Determine the break$-$even point for the two methods, using a rate of return $=25\%.$

Things to calculate:

$($A$/$P$,25\%,10),$ variation cost, automated and machine cost

A South Africa Company 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 $250$ 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 $2$ minute $($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 $(3000$ hr$/$yr$.),$ determine:

$($a$)$ How many production operations,

$($b$)$ How many workers will be required in the plant and

$($c$)$ How much floor space.