Sophia operates a full-service day spa in a small college town. She rented space next to her spa and opened a spray tanning salon. She initially expected tanning costs to be mostly fixed, but noticed total costs increased with the number of appointments. The past 8 months of data are:

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

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

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Required

1) Which month represents the high point (by activity)? Which month represents the low point?

• High point: _________

• Low point: _________

2) Using the high–low method, compute:

• Variable rate per tanning appointment (round to the nearest cent): $ ______ per appointment

• Fixed cost per month (round to the nearest dollar): $ ______ per month

3) Using the variable rate and fixed cost from (2), write the cost formula for tanning services:

Total Cost=Fixed Cost per Month+(Variable Rate × Appointments)

4) Using the formula from (3), predict total cost for September for 2,500 appointments. Of that total, state the total fixed cost and the total variable cost for September. (Round final dollar amounts to the nearest dollar.)

• Total predicted cost for September: $ ______

• Total fixed cost for September: $ ______

• Total predicted variable cost for September: $ ______

5) Using the same formula, predict total cost for September for 3,910 appointments. (Round to nearest dollar.)

• Total predicted cost for September: $ ______

While the total cost prediction in this part is [greater/less] than the prediction from Requirement 4, Sophia should be concerned because 3,910 appointments is [higher/lower] than the highest number of tanning appointments (3,100) contained in the 8 months of data on which the high–low method is based.

• Choose the correct words and fill the blanks: [greater/less], [higher/lower].

6) Which of the following statements is correct regarding the high–low method?

a) It uses only the highest and lowest activity months and can be distorted if those months are atypical.
b) It uses all data points, so it is always more accurate than regression.
c) It determines variable cost per unit by dividing total cost by total units.
d) It captures non-linear and step-cost behavior better than other methods.