Question

worthington hills grocery store has five regular checkout lines and one express line (12 items or less). based on a sampling study, it takes 15 minutes on the average for a customer to go through the regular line and 4 minutes to go through the express line. the store is open from 9 a.m. to 9 p.m. daily.

a. what is the stores maximum capacity (customers processed per day)? round your answer down to the nearest whole number.

420 customers processed per day

b. what is the stores capacity by day of the week if the five regular checkout lines operate according to the schedule below (the express line is always open)? do not round intermediate calculations. round your answers down to the nearest whole number.

hours/day mon tue wed thur fri sat sun
9 - 12 a.m. 1 2 1 2 2 4 3
12 - 4 p.m. 2 1 3 2 4 5 4
4 - 6 p.m. 4* 4 3 3 5 4 2
6 - 9 p.m. 4 3 4 3 5 4 1

• a \3\ means three regular checkout lines are open on monday from 4 to 6 p.m.

the stores capacity by day of the week (customers per day):
hours mon tue wed thur fri sat sun
totals 288 312 296 368 388 308

Explanation:

Step1: Calculate daily capacity of express - line

The store is open from 9 a.m. to 9 p.m., so it is open for 12 hours a day. The express - line takes 4 minutes per customer. In 1 hour (60 minutes), the number of customers processed by 1 express - line is $\frac{60}{4}=15$ customers. In 12 hours, the number of customers processed by 1 express - line is $15\times12 = 180$ customers.

Step2: Calculate daily capacity of regular lines

There are 5 regular lines. Each regular line takes 15 minutes per customer. In 1 hour (60 minutes), the number of customers processed by 1 regular line is $\frac{60}{15}=4$ customers. In 12 hours, the number of customers processed by 5 regular lines is $4\times5\times12=240$ customers.

Step3: Calculate maximum daily capacity

The maximum daily capacity is the sum of the customers processed by regular lines and express - line. So, it is $180 + 240=420$ customers.

Step4: Calculate capacity for Monday

For Monday:

• 9 - 12 a.m. (3 hours), 1 regular line open: $1\times4\times3 = 12$ customers
• 12 - 4 p.m. (4 hours), 2 regular lines open: $2\times4\times4 = 32$ customers
• 4 - 6 p.m. (2 hours), 3 regular lines open: $3\times4\times2 = 24$ customers
• 6 - 9 p.m. (3 hours), 4 regular lines open: $4\times4\times3 = 48$ customers

The total number of customers processed by regular lines on Monday is $12+32 + 24+48=116$ customers.
The express - line processes 180 customers per day.
So, the total capacity on Monday is $116+180 = 296$ customers.

Answer:

a. 420
b. Mon: 296, Tue: 288, Wed: 312, Thur: 296, Fri: 368, Sat: 388, Sun: 308