Problem$3.$ The Baze Pizza in Johnson Center accepts eat$-$in orders and in$-$app orders dellivered by robots at an average rates of $30$ and $40$ orders$/$hour$,$ respectively. While a walk$-$in order needs to wait an average of $5$ min actually placing the order with a staff member, an in$-$app order can start placing the order via a mobile app immediately after login$.$ According to the store's orders monitoring system, there are on average $2$ walkin orde app orders being placed at any given time. Once an order is placed no matter via walk$-$in or mobile app, a staff member will take the order either to the table $($for walk$-$in orders$)$ or to the robot $($for in$-$app orders$)$ on a first served basis. Assume that on average it takes the same amount of time for a staff member to take a walk$-$in order to the table and an in$-$app order to the delivery robot. The monitoring system shows that there are on avera waiting to be taken to the table or robot. Suppose the entire process is stable. Please answer the following questions by applying the Little's Law.

$($a$)$ Assuming an in$-$app order customer leaves the app right after placing an order, please estimate on average how long a customer spends in placing an in$-$app order?

$($b$)$ Assuming a walk$-$in customer leaves the order counter right after getting his$/$her order placed, please estimate on average how many walk$-$in customers are waiting in Baze Piza?

$($c$)$ What is the average time that a placed order needs to wait before appearing on the table or in a delivery robot?

$($d$)$ How long does it take for an in$-$app order to be ready for robot delivery since the customer logs in the app?

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