Simon Tam is negotiating passage on Serenity as a clandestine fugitive from
the planet Persephone. He is told that the 185 million kilometer trip to Osiris
will cost $4,120. Alternatively, he can take a 365 million kilometer trip to
Bellerophon, but that will cost $7,360. If cost depends on distance, what is
the fixed cost, and what is the variable cost, of the voyage to Bellerophon?
Hi I am having trouble distinguishing what the variable cost would be, so if you could help me out that would be great!!
Of course, I'd be happy to help you understand the concept of variable cost and how it applies to this situation.
In this scenario, Simon Tam has two options for his trip: a shorter trip to Osiris and a longer trip to Bellerophon. The cost is determined based on the distance traveled. Thus, we can assume that the cost is proportional to the distance covered.
To determine the fixed and variable costs, we need to understand the equation that relates the cost with the distance. Let's denote the total cost as C and the distance traveled as D. Based on the information given, we can set up the following equation for the cost:
C = k * D
In this equation, "k" represents the variable cost per kilometer. The variable cost is the cost that changes with the distance traveled.
Now, let's use the information provided to solve for the fixed and variable costs for the trip to Bellerophon.
For the trip to Osiris, we know that the distance is 185 million kilometers and the cost is $4,120. We can substitute these values into the equation:
$4,120 = k * 185 million
Simplifying this equation, we can solve for the variable cost per kilometer (k):
k = $4,120 / 185 million
Similarly, for the trip to Bellerophon, we have a distance of 365 million kilometers and a cost of $7,360:
$7,360 = k * 365 million
Again, simplifying the equation, we can solve for the variable cost per kilometer (k).
k = $7,360 / 365 million
By comparing the variable costs for both trips, we can determine the fixed cost. The fixed cost is the component of the cost that remains constant regardless of the distance traveled. It can be found by subtracting the variable cost per kilometer from the total cost for either trip.
For example, let's use the variable cost per kilometer for the Bellerophon trip (k = $7,360 / 365 million) in the equation:
Fixed Cost = Total Cost - (Variable Cost per kilometer * Distance)
Fixed Cost = $7,360 - (k * 365 million)
By substituting the value of k into the equation, we can solve for the fixed cost.
I hope this clarifies the concept of variable cost and how it applies to the given scenario! Let me know if there's anything else I can assist you with.