do it in excel with formuals $.$ The 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 and big$-$box stores. 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 line 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 orders in queue is limited to a maximum of $30.$ Each order over the $30$th is sent to a subcontractor, at a unit cost of $$5,000.$ In addition, customer contracts stipulate that each day that an order waits to be processed costs $$2,500$ in penalty charges.

$[4$ points$]$

How many additional lines would have to be activated if we wanted to route at most one $(1)$ order per day to a subcontractor?

Hints: Use Scenario $0$ row $($and others, if necessary$)$ for the initial model. Enter the arrival rate, service rate, # of servers and queue capacity in columns B to E and observe the results.

Think $(1)$: What needs to be changed to model the addition of an extra line?

Think $(2)$: For which values are there $1$ order per day sent to the subcontractor?

$[2$ points$]$

If they operated with $10$ active production lines $($i$.$e$.5$ additional lines$),$ what would be the total cost per day? Include costs of additional lines, penalty costs and subcontracting costs.

Hints: Use use one or more row$($s$)$ for the model. Enter arrival rate, service rate, # of servers and queue capacity in columns B to E$.$ Copy the$$ formulas from$$ F$4$:M$4$ to the new rows to obtain the performance measurements. In columns N to P$,$ enter the formulas for each cost component. The Cost:Total $($Q$)$ will add them automatically.

$[2$ points$]$

Suppose that they have improved their manufacturing process and lowered the average time to complete an order to $4$ days. With $10$ active production lines, how much will they save?