Complete Question:
Two new rides are being compared by a local amusement park in terms of their annual operating costs. The two rides are assumed to be able to generate the same level of revenue (and thus the focus on costs). The Tummy Tugger has fixed costs of $10,000 per year and variable costs of $2.50 per visitor. The Head Buzzer has fixed costs of $4000 per year, and variable costs of $4 per visitor. Provide answers to the following questions so the amusement park can make the needed comparison.
Requirement:
Mathematically determine the breakeven number of visitors per year for the two rides to have equal annual costs.
Answer:
4000 visitors
Step-by-step explanation:
As we know that:
Total Annual Cost = Variable Cost Per Unit * Total Units + Fixed Costs
For Tummy Tugger,
Variable Cost per Unit is $2.5 per visitor
Total Units are not given so we assume it to be "x"
Fixed cost is $10,000
By putting values we have:
Total Annual Cost = $2.50x + $10,000 ........ Equation 2
Similarly for Head Buzzer,
Variable Cost per Unit is $4 per visitor
Total Units are not given so we assume it to be "x"
Fixed cost is $4,000
By putting values we have:
Total Annual Cost = $4x + $4,000 .......... Equation 3
As per the requirement, the annual cost for both of the rides is same for the year, which means that Equation 2 is equal to Equation 3.
Mathematically,
2.50x + 10000 = $4x + 4000
$10,000 - $4,000 = $4x - $2.5x
$6,000 = $1.5x
x= $6,000 / $1.5 per unit = 4,000 Units
At 4000 visitors for a year, the annual cost of both rides is the same.