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 (therefore the focus on costs). The Tummy Tugger has a fixed cost of $10,000 per year and a variable cost of

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.

4000 visitors

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.