e restaurant is open from $6$ p$.$m$.$ to $10$ p$.$m$.$ each night $($except Monday$)$ and, on average, has $28$ customers enter the bar and $56$ enter the dining room at the beginning of each of those hours. Taylor has noticed the trends over the last $2$ years and expects that within about $4$ years, the number of bar customers will increase by $50\%$ and the dining customers will increase by $20\%.$ Taylor is worried that the restaurant will be not be able to handle the increase and has asked you to study its capacity. In your study, you consider four areas of capacity: the parking lot $($which has $86$ spaces$),$ the bar $(60$ seats$),$ the dining room $(106$ seats$),$ and the kitchen. The kitchen is well$-$staffed and can prepare any meal on the menu in an average of $12$ minutes per meal. The kitchen, when fully staffed, is able to have up to $20$ meals in preparation at a time, or $100$ meals per hour $(60$ minute$/12$ minute $\backslash$times $20$ meals$).$ To assess the capacity of the restaurant, you obtain the additional information:

Diners typically come to the restaurant by car, with an average of $3$ persons per car, while bar patrons arrive with an average of $1\mathrm{.}5$ persons per car.

Diners, on average, occupy a table for an hour, while bar customers usually stay for an average of $2$ hours.

Due to fire regulations, all bar customers must be seated.

The bar customer typically orders one drink per hour at an average of $$7$ per drink; the dining room customer orders a meal with an average price of $$22$; the restaurant$$s cost per drink is $$1,$ and the direct costs for meal preparation are $$5.$

Required:

$1-$a$.$ Given the current number of customers per hour, what is the amount of excess capacity in the bar, dining room, parking lot, and kitchen?

$1-$b$.$ Calculate the expected total throughput margin for the restaurant per day, and month $($assuming a $26-$day month$).$

$2-$a$.$ Given the expected increase in the number of customers, determine if there is a constraint for any of the four areas of capacity. What is the amount of needed capacity for each constraint?

$2-$b$.$ If there is a constraint, reduce the demand on the constraint so that the restaurant is at full capacity $($assume some customers would have to be turned away$).$ Calculate the expected total throughput margin for the restaurant per day, and month $($assuming a $26-$day month$).$