Cathy Gwynn, a recently graduated engineer, decided to invest some of her money in a "Quick Shop" grocery store. The store emphasizes quick service, a limited assortment of grocery items, and rather high prices. Cathy wants to study the business to see if the store hours (currently 0600 to 0100) can be changed to make the store more profitable. Cathy assembled the following information.
Time Period Daily Sales in the Time Period
0600-0700............................................. ¢ 20
0700-0800................................................ 40
0800-0900................................................ 60
0900-1200.............................................. 200
1200-1500.............................................. 180
1500-1800.............................................. 300
1800-2100.............................................. 400
2100-2200.............................................. 100
2200-2300................................................ 30
2300-2400................................................ 60
2400-0100................................................ 20
The cost of the groceries sold averages 70% of sales. The incremental cost to keep the store open, including the clerk's wage and other incremental operating costs, is $10 per hour. To maximize profit, when should the store be opened, and when should it be closed?