Chapter 10, Problem 8PA

(a)

Summary Introduction

Interpretation:The maximum capacity of store per day needs to be calculated with the help of given data.

Concept Introduction: Capacity measurement is an important concept which helps companies to make long term and short-term decisions related to capacity and thus plan for contingencies.

Explanation of Solution

A.

Given Information:

There are 5 regular lines ad 1 express lines.

Average time a customer spends in a regular line = 11 min which means that one regular line can handle 5.45 customers per day.

Average time a customer spends in an express line = 4 min which means that one express line can handle 15 customers per day.

Shift duration = 12 hours per day

Thus,

The capacity of 5 regular lines = $\text{5}\text{.45 }\times \text{ 12 }\times \text{ 5 = 327 customers per day}$

The capacity of 1 express lines = $\text{15 }\times \text{ 12 }\times \text{ 1 = 180 customers per day}$

Therefore, the maximum capacity of store = (327 + 180) = 507 customers per day.

B.

Summary Introduction

Interpretation:The maximum capacity of store per day needs to be calculated with the help of given data.

Concept Introduction: Capacity measurement is an important concept which helps companies to make long term and short-term decisions related to capacity and thus plan for contingencies.

Explanation of Solution

Given Information:

There are 5 regular lines ad 1 express lines.

Average time a customer spends in a regular line = 11 min which means that one regular line can handle 5.45 customers per day.

Average time a customer spends in an express line = 4 min which means that one express line can handle 15 customers per day.

Shift duration = 12 hours per day

The store’s capacity by day of the week is as follows:

Period	Monday
	Hours	No. of lines open	Capacity (customers per day)
9-12 noon	3	1	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 1 = 16}\text{.35}$
12-4 PM	4	2	$\text{5}\text{.45 }\times \text{ 4 }\times \text{ 2 = 43}\text{.6}$
4-6 PM	2	3	$\text{5}\text{.45 }\times \text{ 2 }\times \text{ 3 = 32}\text{.7}$
6-9 PM	3	4	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 4 = 65}\text{.4}$
Total Capacity of Regular Line (Customers per day)			158.05

Since the express line is always open, and the capacity is 180 customers per day.

Therefore, the maximum capacity on Monday is 338 customers per day.

Also, the maximum capacity on Tuesday, Wednesday and Thursday will be 338 customers per day as same number of regular lines are open as on Monday.

Period	Friday
	Hours	No. of lines open	Capacity (customers per day)
9-12 noon	3	3	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 3 = 49}\text{.05}$
12-4 PM	4	3	$\text{5}\text{.45 }\times \text{ 4 }\times \text{ 3 = 65}\text{.4}$
4-6 PM	2	5	$\text{5}\text{.45 }\times \text{ 2 }\times \text{ 5 = 54}\text{.5}$
6-9 PM	3	5	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 5 = 81}\text{.75}$
Total Capacity of Regular Line (Customers per day)			250.7

Since the express line is always open, and the capacity is 180 customers per day.

Therefore, the maximum capacity on Friday is 431 customers per day.

Period	Saturday
	Hours	No. of lines open	Capacity (customers per day)
9-12 noon	3	5	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 5 = 81}\text{.75}$
12-4 PM	4	5	$\text{5}\text{.45 }\times \text{ 4 }\times \text{ 5 = 109}$
4-6 PM	2	3	$\text{5}\text{.45 }\times \text{ 2 }\times \text{ 3 = 32}\text{.7}$
6-9 PM	3	3	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 3 = 49}\text{.05}$
Total Capacity of Regular Line (Customers per day)			272.5

Since the express line is always open, and the capacity is 180 customers per day.

Therefore, the maximum capacity on Saturday is 452.5 customers per day.

Period	Sunday
	Hours	No. of lines open	Capacity (customers per day)
9-12 noon	3	2	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 2 = 32}\text{.7}$
12-4 PM	4	4	$\text{5}\text{.45 }\times \text{ 4 }\times \text{ 4 = 87}\text{.2}$
4-6 PM	2	2	$\text{5}\text{.45 }\times \text{ 2 }\times \text{ 2 = 21}\text{.8}$
6-9 PM	3	1	$\text{5}\text{.45 }\times \text{ 3 }\times \text{ 1 = 16}\text{.35}$
Total Capacity of Regular Line (Customers per day)			158.05

Since the express line is always open, and the capacity is 180 customers per day.

Therefore, the maximum capacity on Sunday is 338.5 customers per day.