Sophia operates a full service day spa in a small college town. Recently, Sophia rented space next to her spa and opened a spray tanning salon. She

anticipated that the costs for the spray tanning service would primarily be fixed, but found that tanning salon costs increased with the number of

appointments. Costs for this service over the past $8$ months are as follows:

Required:

Which month represents the high point? The low point?

High point

Low point

Using the high$-$low method, compute the variable rate for tanning$.$ Next, compute the fixed cost per month. Round the variable rate per tanning

appointment to the nearest cent.

Which month represents the high point? The low point?

High point

Low point

Using the high$-$low method, compute the variable rate for tanning$.$ Next, compute the fixed cost per month. Round the variable rate per tanning

appointment to the nearest cent.

Variable rate for tanning

per tanning appointment

Fixed cost per month $

Using the variable rate and fixed cost, what is the cost formula for tanning services?

Calculate the total predicted cost of tanning services for September for $1,650$ appointments using the formula found in Requirement $3.$ Of that total

cost$,$ how much is the total fixed cost for September? How much is the total predicted variable cost for September? In your calculations, round

variable cost per unit to the nearest cent. If required, round the final answers to the nearest dollar.

Total predicted cost for September

Total fixed cost for September

Total predicted variable for September

Calculate the total predicted cost of tanning services for September for $2,100$ appointments.

While the total cost prediction is

: greater than the prediction from Requirement $4,$ Sophia should be concerned that the number

of tanning appointments of $2,100$ in this calculation is$.$

than the highest number of tanning appointments $(1,700)$ contained in

the $8$ months of data upon which the high$-$low method constructed the cost function.

Which of the following statements is correct when Sophia uses the high$-$low method to estimate the costs?