Answer:
The problem presents two companies, Company A and Company B, offering rental services for a truck. These companies have different pricing structures for renting the same truck. Let’s compare the two options.
Option 1: Company A charges $150 per day plus $0.20 per mile.
Option 2: Company B charges $70 per day plus $0.40 per mile.
To determine which option is better, we need to establish the conditions under which one option becomes less expensive than the other.
First, we must determine the breakeven point - the point at which the costs of renting from Company A equal the costs of renting from Company B.
Let’s assume the number of miles driven is represented by ‘x’.
For Company A, the total cost (C1) would be given by:
C1 = $150 (daily rate) + $0.20 (mileage rate) * x (number of miles driven)
For Company B, the total cost (C2) would be given by:
C2 = $70 (daily rate) + $0.40 (mileage rate) * x (number of miles driven)
To find the breakeven point, we need to equate C1 and C2:
$150 + $0.20x = $70 + $0.40x
Now, let’s solve the equation to find the value of ‘x’ when the costs are equal:
$0.20x - $0.40x = $70 - $150
-$0.20x = -$80
x = -$80 / -$0.20
x = 400 miles
Therefore, if the rental involves driving more than 400 miles, it is more cost-effective to choose Company B. Conversely, if the rental requires driving less than 400 miles, it is more economical to rent from Company A.
Note: It’s important to compare other factors, such as the quality of service, reputation, terms and conditions, and additional charges, before making a final decision.