An online grocery store is expanding to a new city. Shoppers place orders

online and their groceries are delivered by purpose-built drones. Drones

were chosen because they will not be affected by ground-based traffic. While

the service is new, it is expected to grow in popularity, specially with customers

in the 2040 year-old range. A representative map of the city was

constructed with each box representing a neighbourhood.

G

275

C

25

H

514

D

971

B

433

I

1343

N

522

O

1520

J

2287

K

3129

P

1960

R

798

Q

493

S

667

V

815

E

3273

F

2717

U

582

L

2142

M

275

T

299

W

85

A

75

X

35

The number in each box represents the estimated number of potential customers

in that neighbourhood. The following table contains the coordinates

(x; y) of each population box (neighbourhood):

Box (x; y) Box (x; y) Box (x; y) Box (x; y)

A (1; 6) B (2; 6) C (2; 5) D (3; 5)

E (5; 5) F (6; 5) G (1; 4) H (2; 4)

I (3; 4) J (4; 4) K (5; 4) L (6; 4)

M (7; 4) N (2; 3) O (3; 3) P (4; 3)

Page 1 of 5

Box (x; y) Box (x; y) Box (x; y) Box (x; y)

Q (3; 2) R (4; 2) S (5; 2) T (6; 2)

U (3; 1) V (4; 1) W (6; 1) X (7; 1)

(a) Considering only proximity to customers, suggest the neighbourhood in

which a distribution centre should be located. [Hint: Round your (x; y)

coordinates to the nearest integer when determining a suitable neighbourhood.]

The company was concerned that customers living in neighbourhoods with

higher population density have more grocery buying options and would therefore

be less likely to use its services. To gather a better understanding, a survey

was conducted to find the proportion of potential customers that would

use the service. The results are tabulated in the following table:

Box Expected Box Expected Box Expected Box Expected

Usage (%) Usage (%) Usage (%) Usage (%)

A 95 B 95 C 95 D 90

E 25 F 30 G 95 H 95

I 70 J 60 K 25 L 35

M 35 N 90 O 60 P 50

Q 90 R 85 S 85 T 95

U 85 V 85 W 95 X 95

(b) Considering the distribution of expected customers (taking into account

the probability of usage) re-evaluate the placement of the distribution

centre.

(c) Which of the two options calculated in parts (a) and (b) would you

choose and why?