
Concept explainers
a.
To write and graph the rational function representing Liam’s average cost per customer as a function of number of parking lots
a.

Answer to Problem 36PPS
The rational function that represents Liam’s average cost per customer as a function of number of parking lots is f(x)=50x+4500x and graph for this function is represented
Explanation of Solution
Given information:
Liam purchased a snow plow for $4500 and he incurs a cost of $50 for gas and maintenance when he plows the parking lots each time.
The snow plow cost $4500 and he incurs a cost of $50 for gas and maintenance when he mows a lawn.
Thus, the total cost on Liam’s part is 50x+4500
This means that the average cost for x customers is,
50x+4500x
Therefore, the function that represents his average cost per customer as a function of the number of parking lots mowed is,
f(x)=50x+4500x
The graph of the function can be represented as,
b.
To find out the asymptotes of the graph
b.

Answer to Problem 36PPS
The vertical asymptote is x=0
Explanation of Solution
Given information:
Liam purchased a snow plow for $4500 and he incurs a cost of $50 for gas and maintenance when he plows the parking lots each time.
Rational function of average cost per parking lot is f(x)=50x+4500x
To find the vertical asymptotes, set the denominator equal to zero
So, put x=0
Therefore, the vertical asymptote is x=0
c.
To explain why the first quadrant in the graph is the only relevant quadrant
c.

Answer to Problem 36PPS
The first quadrant in the graph is only relevant because x represents the number of parking lawns mowed and its value cannot be negative
Explanation of Solution
Given information:
Liam purchased a snow plow for $4500 and he incurs a cost of $50 for gas and maintenance when he plows the parking lots each time.
The number of parking lots mowed is x .
Thus, its value cannot be negative.
Hence, the only part of the graph that is relevant is the one in the first quadrant.
d.
To find out the total number of parking lot Liam need to plow for his average cost per parking lot is less than $80
d.

Answer to Problem 36PPS
Liam need to plow less than 150 times for his average cost per parking lot to be less than $80
Explanation of Solution
Given information:
Liam purchased a snow plow for $4500 and he incurs a cost of $50 for gas and maintenance when he plows the parking lots each time.
Rational function of average cost per parking lot is f(x)=50x+4500x
For the cost to be less than $80 the function must be written as,
f(x)<804500+50xx<80
The obtained function must be solved as,
80−4500+50xx>080x−4500−50xx>030x−4500x>030(x−150)x>0(x−150)x>0⇒x∈(−∞,0)∪(150,∞)
As x>0 , it means the solution is x>150
Chapter 8 Solutions
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