You are playing the "Root Beer Game" simulation with the above supply chain.$$Let$$s assume that all members of the supply chain have $100,000$ cases of root beer in their inventory.$$Members of the chain are allowed to ship partial orders while they wait for the remainder of the order to arrive from upstream in the chain. A Customer walks into the Retailer and orders $810,000$ cases of root beer. How many weeks will it take for the Customer to receive their entire order of root beer according to the following specifications?

Order Processing Delay$2$ week$($s$)$Shipping Delay$1$ week$($s$)$Factory Production Delay$2$ week$($s$)$

Please answer using just a number like $"17"$ instead of $"17$ weeks".

The answer is not $5$