Penne Pesto is a small restaurant in the financial district of San Francisco. Customers order from a variety of pasta dishes. The restaurant has $80$ seats and is always full during the four hours in the evening. It is not possible to make reservations at Penne; most guests show up spontaneously on their way home from work. If there is no available seat, guests simply move on to another place. On average, a guest spends $78$ minutes in the restaurant, which includes $4$ minutes until the guest is seated and the waiter has taken the order, an additional $9$ minutes until the food is served, $59$ minutes to eat, and $6$ minutes to handle the checkout $($including waiting for the check, paying, and leaving$).$ It takes the restaurant another $18$ minutes to clean the table and have it be ready for the next guests $($of which there are always plenty$).$ The average guest leaves $$24$ at Penne, including food, drink, and tip $($all tips are collected by the restaurant; employees get a fixed salary$).$ The restaurant has $10$ waiters and $10$ kitchen employees, each earning $$90$ per evening $($including any preparation, the $4$ hours the restaurant is open, and cleanup$).$ The average order costs $$5\mathrm{.}2$ in materials, including $$4\mathrm{.}0$ for the food and $$1\mathrm{.}2$ for the average drink. In addition to labor costs, fixed costs for the restaurant include $$550$ per day of rent and $$400$ per day for other overhead costs. The restaurant is open $365$ days a year and is full to the last seat even on weekends and holidays. There is about $$573,000$ of capital tied up in the restaurant, largely consisting of furniture, decoration, and equipment. a$.$ How many guests will the restaurant serve in one evening? b$.$ What is the return on invested capital $($ROIC$)$ for the owner of the restaurant? $($Round your answer to two decimal places.$)$ c$.$ Assume that you could improve the productivity of the kitchen employees and free up one person who would be helping to clean up the table. This would reduce the cleanup to $6$ minutes instead of $10$ minutes. What would be the new ROIC? $($Round your answer to nearest whole number.$)$ d$.$ What would be the new ROIC if overhead charges could be reduced by $$100$ per day? $($Round your answer to one decimal place.$)$