Question

1. the function ( c(x)=35x + 75 ) represents the labor cost (in dollars) for bobs auto repair to replace your alternator, where ( x ) is the number of hours of labor. the table shows sample labor costs from its main competitor, budget auto repair. the alternator is estimated to take 5 hours of labor. which company would you hire? explain.

Explanation:

Step1: Find the cost function for Budget Auto Repair

Let the cost function for Budget Auto Repair be \(C_{1}(x)=mx + b\). Using the points \((1,90)\) and \((2,130)\):
The slope \(m=\frac{130 - 90}{2 - 1}=40\).
Substitute \(x = 1\), \(m = 40\) and \(C_{1}(1)=90\) into \(C_{1}(x)=mx + b\):
\(90=40\times1 + b\), so \(b = 50\). Then \(C_{1}(x)=40x + 50\).

Step2: Calculate the cost for 5 - hour labor for each company

For Bob's Auto Repair: \(C(x)=35x + 75\). When \(x = 5\), \(C(5)=35\times5+75=175 + 75=250\).
For Budget Auto Repair: \(C_{1}(x)=40x + 50\). When \(x = 5\), \(C_{1}(5)=40\times5+50=200 + 50=250\).

Answer:

You can hire either company as the cost is the same (\(\$250\)) for 5 hours of labor.