Question 7 (20marks) A famous old-style diner in the South Loop district of downtown Chicago is the Blackstone Grill. It is medium-size, with a total of 65 seats arranged in two-person tables or four-person booths. The Grill is open from 6 a.m. to 12 p.m., serving breakfast, lunch, and dinner, 28 days per month. The Grill rents its premises from the Blackstone Hotel for $7,000 per month, which includes all water and electricity. It pays $500 each month on a long-term bank loan that was used to purchase its ovens, grill, refrigerators, and other equipment. Insurance and license fees come to about $500 per month. The owner has hired 8 employees to work at the Grill. A manager both supervises the employees and is responsible for accounting and payroll functions. She earns $3,000 per month. The cook gets $2,500, and the 6 people who wait on tables, bus, and wash the dishes each earn a base salary of $1,500 per month and split the tips evenly. 1. If the average customer's bill is $4.25 and the food that is purchased by the Grill represents 30% of the cost of a meal, how many customers must the Grill get each month to break even? II. Consider now the "occupancy rate" of the Grill, which is the percentage of seats that are filled at any particular point in time. Suppose that customers take an average of 45 minutes to eat. What occupancy rate must the Grill have to break even? III. The occupancy of the Grill varies during the course of a day. During the peak hours for breakfast (6:30 to 8:30), lunch, (12:00 to 1:30 p.m.), and dinner (5:30 to 7:30 p.m.), the occupancy is much greater than during the slower periods. Suppose that the Grill has one occupancy rate during the peak periods and another occupancy rate during the slow periods. Write an equation that relates the occupancy rates in these two periods, based on the assumption that the Grill is exactly breaking even. Draw a graph of the off-peak break-even occupancy rate as a function of the peak-period break-even occupancy rate. IV. Suppose that the peak-period occupancy rate is 80% and the off-peak occupancy rate is 25%. Write an equation that you could use to calculate the price that the Blackstone Grill would have to charge for an average meal to break even at those occupancy rates. Solve that equation to find the break-even average price per meal at those rates. Question 7 (20marks) A famous old-style diner in the South Loop district of downtown Chicago is the Blackstone Grill. It is medium-size, with a total of 65 seats arranged in two-person tables or four-person booths. The Grill is open from 6 a.m. to 12 p.m., serving breakfast, lunch, and dinner, 28 days per month. The Grill rents its premises from the Blackstone Hotel for $7,000 per month, which includes all water and electricity. It pays $500 each month on a long-term bank loan that was used to purchase its ovens, grill, refrigerators, and other equipment. Insurance and license fees come to about $500 per month. The owner has hired 8 employees to work at the Grill. A manager both supervises the employees and is responsible for accounting and payroll functions. She earns $3,000 per month. The cook gets $2,500, and the 6 people who wait on tables, bus, and wash the dishes each earn a base salary of $1,500 per month and split the tips evenly. 1. If the average customer's bill is $4.25 and the food that is purchased by the Grill represents 30% of the cost of a meal, how many customers must the Grill get each month to break even? II. Consider now the "occupancy rate" of the Grill, which is the percentage of seats that are filled at any particular point in time. Suppose that customers take an average of 45 minutes to eat. What occupancy rate must the Grill have to break even? III. The occupancy of the Grill varies during the course of a day. During the peak hours for breakfast (6:30 to 8:30), lunch, (12:00 to 1:30 p.m.), and dinner (5:30 to 7:30 p.m.), the occupancy is much greater than during the slower periods. Suppose that the Grill has one occupancy rate during the peak periods and another occupancy rate during the slow periods. Write an equation that relates the occupancy rates in these two periods, based on the assumption that the Grill is exactly breaking even. Draw a graph of the off-peak break-even occupancy rate as a function of the peak-period break-even occupancy rate. IV. Suppose that the peak-period occupancy rate is 80% and the off-peak occupancy rate is 25%. Write an equation that you could use to calculate the price that the Blackstone Grill would have to charge for an average meal to break even at those occupancy rates. Solve that equation to find the break-even average price per meal at those rates