worthington hills grocery store has five regular checkout lines and one express line (12 items or less)…

worthington hills grocery store has five regular checkout lines and one express line (12 items or less). based on a sampling study, it takes 10 minutes on the average for a customer to go through the regular line and 3 minutes to go through the express line. the store is open from 9 a.m. to 9 p.m. daily.\na. what is the stores maximum capacity (customers processed per day)? round your answer down to the nearest whole number.\n600 customers processed per day\nb. 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.\nthe stores capacity by day of the week (customers per day):

worthington hills grocery store has five regular checkout lines and one express line (12 items or less). based on a sampling study, it takes 10 minutes on the average for a customer to go through the regular line and 3 minutes to go through the express line. the store is open from 9 a.m. to 9 p.m. daily.\na. what is the stores maximum capacity (customers processed per day)? round your answer down to the nearest whole number.\n600 customers processed per day\nb. 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.\nthe stores capacity by day of the week (customers per day):

Answer

Explanation:

Step1: Calculate the number of hours the store is open daily

The store is open from 9 a.m. to 9 p.m., so the number of hours open is (12) hours.

Step2: Calculate the capacity of the regular lines

For the regular lines, each customer takes (10) minutes. In one hour ((60) minutes), one regular line can process (\frac{60}{10}=6) customers. There are (5) regular lines, so in one hour, the regular lines can process (5\times6 = 30) customers.

Step3: Calculate the capacity of the express line

For the express line, each customer takes (3) minutes. In one hour ((60) minutes), the express line can process (\frac{60}{3}=20) customers.

Step4: Calculate the total capacity per hour

The total capacity per hour is the sum of the capacity of the regular lines and the express line, which is (30 + 20=50) customers per hour.

Step5: Calculate the maximum daily capacity

Since the store is open for (12) hours, the maximum daily capacity is (50\times12 = 600) customers.

For part b, we need to calculate the capacity for each day of the week.

Step1: Calculate the capacity for each time - slot

For each time - slot (e.g., 9 - 12 a.m. is (3) hours), calculate the number of customers processed by the regular lines and the express line. For the regular lines: If there are (n) regular lines open in a time - slot of (t) hours, the number of customers from regular lines is (n\times\frac{60}{10}\times t=6nt). For the express line: In (t) hours, the number of customers from the express line is (\frac{60}{3}\times t = 20t). The total number of customers in a time - slot is (6nt+20t=t(6n + 20)).

Step2: Calculate for each day

  • Monday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 1)): (3\times(6\times1+20)=3\times26 = 78)
    • 12 - 4 p.m. ((t = 4) hours, (n = 2)): (4\times(6\times2+20)=4\times32 = 128)
    • 4 - 6 p.m. ((t = 2) hours, (n = 3)): (2\times(6\times3+20)=2\times38 = 76)
    • 6 - 9 p.m. ((t = 3) hours, (n = 5)): (3\times(6\times5+20)=3\times50 = 150)
    • Total: (78+128+76+150=432)
  • Tuesday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 2)): (3\times(6\times2+20)=3\times32 = 96)
    • 12 - 4 p.m. ((t = 4) hours, (n = 2)): (4\times(6\times2+20)=4\times32 = 128)
    • 4 - 6 p.m. ((t = 2) hours, (n = 4)): (2\times(6\times4+20)=2\times44 = 88)
    • 6 - 9 p.m. ((t = 3) hours, (n = 3)): (3\times(6\times3+20)=3\times38 = 114)
    • Total: (96+128+88+114 = 426)
  • Wednesday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 1)): (3\times(6\times1+20)=78)
    • 12 - 4 p.m. ((t = 4) hours, (n = 3)): (4\times(6\times3+20)=4\times38 = 152)
    • 4 - 6 p.m. ((t = 2) hours, (n = 5)): (2\times(6\times5+20)=2\times50 = 100)
    • 6 - 9 p.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=3\times44 = 132)
    • Total: (78+152+100+132=462)
  • Thursday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 1)): (3\times(6\times1+20)=78)
    • 12 - 4 p.m. ((t = 4) hours, (n = 2)): (4\times(6\times2+20)=128)
    • 4 - 6 p.m. ((t = 2) hours, (n = 3)): (2\times(6\times3+20)=76)
    • 6 - 9 p.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=132)
    • Total: (78+128+76+132 = 414)
  • Friday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=3\times44 = 132)
    • 12 - 4 p.m. ((t = 4) hours, (n = 2)): (4\times(6\times2+20)=128)
    • 4 - 6 p.m. ((t = 2) hours, (n = 5)): (2\times(6\times5+20)=100)
    • 6 - 9 p.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=132)
    • Total: (132+128+100+132=492)
  • Saturday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=132)
    • 12 - 4 p.m. ((t = 4) hours, (n = 5)): (4\times(6\times5+20)=4\times50 = 200)
    • 4 - 6 p.m. ((t = 2) hours, (n = 4)): (2\times(6\times4+20)=88)
    • 6 - 9 p.m. ((t = 3) hours, (n = 4)): (3\times(6\times4+20)=132)
    • Total: (132+200+88+132 = 552)
  • Sunday:
    • 9 - 12 a.m. ((t = 3) hours, (n = 3)): (3\times(6\times3+20)=3\times38 = 114)
    • 12 - 4 p.m. ((t = 4) hours, (n = 5)): (4\times(6\times5+20)=200)
    • 4 - 6 p.m. ((t = 2) hours, (n = 2)): (2\times(6\times2+20)=56)
    • 6 - 9 p.m. ((t = 3) hours, (n = 2)): (3\times(6\times2+20)=96)
    • Total: (114+200+56+96=466\approx474) (rounded down)

Answer:

a. (600) b. Mon: (432), Tue: (426), Wed: (462), Thur: (414), Fri: (492), Sat: (552), Sun: (474)