To calculate the cost to run Unit A per hour, let's break down the problem into a series of steps:
### Step 1: Calculate the Total Hours Worked by Each Unit Over the Three Months
For Unit A:
- June: 184 hours
- July: 174 hours
- August: 168 hours
- Total Hours for Unit A:
[tex]\( 184 + 174 + 168 = 526 \)[/tex] hours
For Unit B:
- June: 207 hours
- July: 198 hours
- August: 189 hours
- Total Hours for Unit B:
[tex]\( 207 + 198 + 189 = 594 \)[/tex] hours
For Unit C:
- June: 276 hours
- July: 264 hours
- August: 242 hours
- Total Hours for Unit C:
[tex]\( 276 + 264 + 242 = 782 \)[/tex] hours
### Step 2: Calculate the Total Hours Worked by All Units Over the Three Months
Total Hours for All Units:
[tex]\[ 526 \text{ (Unit A)} + 594 \text{ (Unit B)} + 782 \text{ (Unit C)} = 1902 \][/tex] hours
### Step 3: Calculate the Total Cost Over the Three Months
Total Cost for All Units:
- June: \[tex]$142.60
- July: \$[/tex]135.96
- August: \[tex]$128.30
- Total Cost:
\( 142.60 + 135.96 + 128.30 = 406.86 \) dollars
### Step 4: Calculate the Cost per Hour for All Units
Cost per Hour for All Units:
\[ \frac{\text{Total Cost}}{\text{Total Hours}} = \frac{406.86 \text{ dollars}}{1902 \text{ hours}} \approx 0.2139 \text{ dollars per hour} \]
### Step 5: Calculate the Cost Attributed to Unit A
Using the cost per hour for all units combined,
\[ \text{Total Cost for Unit A} = \text{Cost per Hour} \times \text{Total Hours for Unit A} \]
\[ \text{Total Cost for Unit A} = 0.2139 \times 526 \approx 112.54 \text{ dollars} \]
Now, to find the cost per hour for Unit A,
### Step 6: Calculate the Cost per Hour for Unit A
\[ \text{Cost per Hour for Unit A} = \frac{\text{Total Cost for Unit A}}{\text{Total Hours for Unit A}} \]
\[ \text{Cost per Hour for Unit A} = \frac{112.54 \text{ dollars}}{526 \text{ hours}} \approx 0.2139 \text{ dollars per hour} \]
So, the cost to run Unit A per hour is approximately \$[/tex]0.2139.
