High$-$Low Method

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:

Month Tanning

Appointments Total Cost

January $700$ $$1,746$

February $2,100$ $$2,110$

March $3,100$ $$2,730$

April $2,400$ $$2,500$

May $1,600$ $$1,800$

June $2,400$ $$2,265$

July $2,190$ $$2,200$

August $3,100$ $$2,630$

Required:

$1.$ Which month represents the high point? The low point?

High point

Low point

In your calculations, round per unit costs to the nearest cent.

$2.$ 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 and use it in your further calculations. Round the fixed cost per month to the nearest dollar and use it in your further calculations.

Variable rate for tanning fill in the blank $1$ of $2$$ per tanning appointment

Fixed cost per month fill in the blank $2$ of $2$$

$3.$ Using the variable rate and fixed cost, what is the cost formula for tanning services?

$4.$ Calculate the total predicted cost of tanning services for September for $2,500$ 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? If required, round the final answers to the nearest dollar.

Line Item Description Amount

Total predicted cost for September $fill in the blank $6$

Total fixed cost for September $fill in the blank $7$

Total predicted variable cost for September $fill in the blank $8$

$5.$ Calculate the total predicted cost of tanning services for September for $3,910$ appointments. If required, round the final answers to the nearest dollar. fill in the blank $1$ of $1$$

While the total cost prediction is

greater than the prediction from Requirement $4,$ Sophia should be concerned that the number of tanning appointments of $3,910$ in this calculation is

than the highest number of tanning appointments $(3,100)$ contained in the $8$ months of data upon which the high$-$low method constructed the cost function.

$6.$ Which of the following statements is correct when Sophia uses the high$-$low method to estimate the costs?

Check My Work$2$ more Check My Work uses remaining.