A company operates a chain of filling stations in each of which are employed cashiers, attendants and mechanics as shown:

Let matrix $P$ represent the number of personnel per type of filling station:

$$P = \begin{bmatrix} 4 & 2 & 1 \\ 12 & 6 & 3 \\ 6 & 4 & 2 \end{bmatrix}$$

The rows represent Cashier, Attendant, and Mechanics, respectively. The columns represent Large, Medium, and Small stations.

Let matrix $S$ represent the number of filling stations of each type in Ebony and Imo:

$$S = \begin{bmatrix} 3 & 7 \\ 5 & 8 \\ 12 & 4 \end{bmatrix}$$

The rows represent Large, Medium, and Small stations, respectively. The columns represent Ebony and Imo locations.

The product $R = P \times S$ will give the total number of personnel for each category in each location.

$$R = \begin{bmatrix} 4 & 2 & 1 \\ 12 & 6 & 3 \\ 6 & 4 & 2 \end{bmatrix} \begin{bmatrix} 3 & 7 \\ 5 & 8 \\ 12 & 4 \end{bmatrix}$$

For Cashiers (Row 1 of $R$):

• Ebony: $(4 \times 3) + (2 \times 5) + (1 \times 12) = 12 + 10 + 12 = 34$
• Imo: $(4 \times 7) + (2 \times 8) + (1 \times 4) = 28 + 16 + 4 = 48$

For Attendants (Row 2 of $R$):

• Ebony: $(12 \times 3) + (6 \times 5) + (3 \times 12) = 36 + 30 + 36 = 102$
• Imo: $(12 \times 7) + (6 \times 8) + (3 \times 4) = 84 + 48 + 12 = 144$

For Mechanics (Row 3 of $R$):

• Ebony: $(6 \times 3) + (4 \times 5) + (2 \times 12) = 18 + 20 + 24 = 62$
• Imo: $(6 \times 7) + (4 \times 8) + (2 \times 4) = 42 + 32 + 8 = 82$

$$R = \begin{bmatrix} 34 & 48 \\ 102 & 144 \\ 62 & 82 \end{bmatrix}$$

This matrix shows:

• Row 1: Total Cashiers for Ebony (34) and Imo (48)
• Row 2: Total Attendants for Ebony (102) and Imo (144)
• Row 3: Total Mechanics for Ebony (62) and Imo (82)

The total number of personnel for each location is:

• For Ebony:
  • Cashiers: 34
  • Attendants: 102
  • Mechanics: 62
• For Imo:
  • Cashiers: 48
  • Attendants: 144
  • Mechanics: 82