To determine which company to hire, let's compare the labor costs of Certified Remodeling and Masterful Remodeling for 8 hours of labor.
### Step 1: Calculate the labor cost for Certified Remodeling
The labor cost function for Certified Remodeling is given by:
[tex]\[ C(x) = 25x + 50 \][/tex]
where [tex]\( x \)[/tex] is the number of hours of labor.
For 8 hours of labor ([tex]\( x = 8 \)[/tex]):
[tex]\[ C(8) = 25(8) + 50 = 200 + 50 = 250 \][/tex]
So, the labor cost for Certified Remodeling for 8 hours of labor is \[tex]$250.
### Step 2: Calculate the labor cost for Masterful Remodeling
The labor costs for Masterful Remodeling are given in the table:
\[
\begin{array}{|c|c|c|c|}
\hline
x & 2 & 4 & 6 \\
\hline
M(x) & 130 & 160 & 190 \\
\hline
\end{array}
\]
We need the labor cost for 8 hours (\( x = 8 \)). Since the table does not provide the cost for 8 hours directly, we'll use linear interpolation to estimate it.
From the table:
- The cost for 2 hours is \$[/tex]130.
- The cost for 4 hours is \[tex]$160.
- The cost for 6 hours is \$[/tex]190.
We observe that the cost increases linearly. Let’s use this linear relationship to find [tex]\( M(8) \)[/tex].
Using a piecewise linear interpolation function based on the given values, the cost for 8 hours can be estimated as:
[tex]\[ M(8) = 220 \][/tex]
So, the labor cost for Masterful Remodeling for 8 hours of labor is \[tex]$220.
### Step 3: Compare the costs
- Certified Remodeling: \$[/tex]250
- Masterful Remodeling: \[tex]$220
### Conclusion
The labor cost for Masterful Remodeling (\$[/tex]220) is less than that for Certified Remodeling (\$250).
Thus, I would hire Masterful Remodeling as they offer a more cost-effective solution for 8 hours of labor.
