Multinational Zimple manufactures a range of electronic products, including the Zim$-$K$,$ a popular state$-$of$-$the$-$art $4$K monitor.

Orders for the Zim$-$K come from online stores and supermarkets. The factory receives an average of $3$ orders a day $($Poisson distribution$).$ Each order is routed to one of the factory's production lines. Whatever its size, an order takes an average of $5$ days to complete $($exponential distribution$)$ on a production line. The factory has $5$ permanently activated production lines, and up to $5$ more can be activated $($total of $10).$ However, each additional chain costs $$1,000$ per day of operation.

To ensure that monitor components are state$-$of$-$the$-$art, inventory is kept to a minimum. Consequently, the number of backorders is limited to a maximum of $30.$ Each order over the $30$th is sent to a subcontractor, at a unit cost of $$5,000.$ In addition, customer contracts stipulate that each day that an order is not processed costs $$2,000$ in penalty charges.