Sure, I'll walk you through the steps of solving this problem based on the information provided.
### 1.2.1 Call-out Fee for Handyman-SA
The call-out fee for Handyman-SA is R450.
### 1.2.2 Hourly Rate for Laws Plumbing
Laws Plumbing charges R550 per hour.
### 1.2.3 Formula for Handyman-SA Company Total Cost
The formula to calculate the total cost for Handyman-SA can be defined as:
[tex]\[ \text{Total cost}(\text{hours}) = \begin{cases}
450, & \text{if hours} \leq 1 \\
450 + ( \text{hours} - 1 ) \times 400, & \text{if hours} > 1
\end{cases}
\][/tex]
### 1.2.4 Calculation of Missing Values G and H
#### (a) The Missing Value G
To find the missing value [tex]\( G \)[/tex] for Handyman-SA for 6 hours:
[tex]\[ G = 450 + (6 - 1) \times 400 \][/tex]
[tex]\[ G = 450 + 5 \times 400 \][/tex]
[tex]\[ G = 450 + 2000 \][/tex]
[tex]\[ G = 2450 \][/tex]
Therefore, the missing value [tex]\( G \)[/tex] is R2450.
#### (b) The Missing Value H
To find the missing value [tex]\( H \)[/tex] for Laws Plumbing for 8 hours:
[tex]\[ H = 8 \times 550 \][/tex]
[tex]\[ H = 4400 \][/tex]
Therefore, the missing value [tex]\( H \)[/tex] is R4400.
### 1.2.5 Cheapest Company for 3 Hours of Work
To determine the cheapest company for 3 hours of work:
Handyman-SA Cost for 3 Hours:
[tex]\[ \text{Cost} = 450 + (3 - 1) \times 400 \][/tex]
[tex]\[ \text{Cost} = 450 + 2 \times 400 \][/tex]
[tex]\[ \text{Cost} = 450 + 800 \][/tex]
[tex]\[ \text{Cost} = 1250 \][/tex]
Laws Plumbing Cost for 3 Hours:
[tex]\[ \text{Cost} = 3 \times 550 \][/tex]
[tex]\[ \text{Cost} = 1650 \][/tex]
Comparing both costs, Handyman-SA charges R1250 while Laws Plumbing charges R1650.
Hence, the cheapest company for 3 hours of work is Handyman-SA, and Joseph will pay R1250 for acquiring the service of the cheapest company.
