Question

Taylor’s is a popular restaurant that offers customers a large dining room and comfortable bar area. Taylor Henry, the owner and manager of the restaurant, has seen the number of patrons increase steadily over the last two years and is considering whether and when she will have to expand its available capacity. The restaurant occupies a large home, and all the space in the building is now used for dining, the bar, and kitchen, but space is available on the property to expand the restaurant. The restaurant is open from 6 p.m. to 10 p.m. each night (except Monday) and, on average, has 30 customers enter the bar and 51 enter the dining room during 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 88 spaces), the bar (66 seats), the dining room (101 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 min/12 min × 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 1.5 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 $8 per drink; the dining room customer orders a meal with an average price of $21; the restaurant’s cost per drink is $2, and the direct costs for meal preparation are $4.

• 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).

Answer 1

Answer 1a) - Straight forward answer . Only challenge in calculation of  "Basis ". Please see below answer for easy reference

Please see calculation basis . Most important factor is calculate to  " Parking Lot " based on Number of hour spend by Customer ( already available in Question)

	Dinning Room	Bar	Parking lot	Kitchen
Measurement base	Seating	Seating	Space	Meals
Calculation Base
Table Occupy( Hr)	1
bar case usually stay(Hr)		2	Dinner - With Avg 3 person per car Bar- Avg 1.5 person per car	1 meal per Dinning customer
			51/3+60/1.5
Current Capacity utilized	51	60	57	51
Actual Capacity	101	66	88	100
Excess Capacity	50	6	31	49

1 b) Throughput Contribution :

Major challenge to calculate Bar capacity . Time to open restaurant - 4 Hrs . We are in assumption that first 1 Hr will be 30 person . after 1 hr over ,, expecting double the capacity of head for rest 3 hrs . We calculate on the same way as below :

Throughput Contribution
Drink Sale( $)	8		Meal Sale( $)	21
Drink Cost( $)	2		Meal Cost( $)	4
Drink Contribution( $)	6		Meal Contribution( $)	17
Source	Calculation	Hours utilized	Contribution(As calculated above )	Contribution /Day	Contribution /Month- 26 days per month
Bar	30*1+60*3	210	6	1260	32760
Dinning - 4 Hrs- 51 Person	51*4	204	17	3468	90168
Time period - 6 PM -10 PM
On the basis of Layover
1 hr @ avg 30
3 hr @ avg 60

Answer 2a) After increased capacity , revised capacity position and shortfall or Excess against Standard capacity . All basis of calculation has been mentioned below :

Please check parking lot calculation base ( same as Question number 1a-explained above) + Bar calculation + kitchen ) all calculation in details as below /;

	Dinning Room	Bar	Parkig lot	Kitchen
Measurement base	Seating	Seating	Space	Meals
Current Capacity utilized	51	30	57
Increased further	20%	50%
Revised Capacity	61.2	90	50	61.2
Actual Capacity	101	66	88	100
Excess/( Shortage Capacity)	40	-24	38	39

Calculation basis - Most Important place to understand  

Parking Lot calculation	Kitchen	bar case usually stay(Hr)
Dinner - With Avg 3 person per car Bar- Avg 1.5 person per car	1 meal per Dinning customer	2 Hr
61/3+45/1.5		Current Capacity -30
50.33		Increased by 50% - revised capacity- 45
		Bar case - 2 hr base
		Derived number - 2hr*45

2b)Final Throughout Margin contribution

Basis of Bar Calculation - As above , we noticed that Bar capacity after increase crossed standard capacity by 24. So we assume that bar area can handle - first 1 hr - 45 Headcount and rest 3 hr max 66 head count

Dinning area - within capacity so they can manage with 61 ( after revised capacity as mentioned above )

Throughput Contribution
Drink Sale( $)	8		Meal Sale( $)	21
Drink Cost( $)	2		Meal Cost( $)	4
Drink Contribution( $)	6		Meal Contribution( $)	17
Soure	Calculation	Hours utilized	Contribution(As calculated above )	Contribution /Day	Contribution /Month- 26 days per month
Bar	45*1+66*3	243	6	1458	37908
Dinning - 4 Hrs- 51 Person	61*4	244	17	4148	107848