Consider a serialized process consisting of $3$ stages: X$,$ Y$,$ and Z$.$ Currently, there is one machine at each stage. Every item must go through all stages.

Stage X is a cutting process; output rate is $45$ units per hour.

Stage Y is an assembly process; output rate is $30$ units per hour.

Stage Z is a polishing process; each unit takes $3$ minutes.

Market demand for this product is $35$ units per hour $(8,400$ units per month$).$ The unit profit margin associated with the sales of the product is $$10.$ Also, assume the following:

Additional machines can be acquired and added to any stage.

Additional machine is identical to the existing one in the stage. Example: If one machine is added to Stage Y $($initially $30$ units per hour$),$ the output rate of Stage Y will increase by $30$ units per hour to $30+30=60$ units per hour.

Cash flows compound monthly to perpetuity, with an annual cost of capital of $15\%.$

$8-$hour daily operation, production runs for $30$ days per month.