Question

Maria Chavez owns a catering company that serves food and beverages at parties and business functions. Chavez’s business is seasonal, with a heavy schedule during the summer months and holidays and a lighter schedule at other times. One of the major events Chavez’s customers request is a cocktail party. She offers a standard cocktail party and has estimated the cost per guest as follows:

Food and beverages	$	16.00
Labor (0.5 hour @ $10.00 /hr.)		5.00
Overhead (0.5 hour @ $18.68/hr.)		9.34
Total cost per guest	$	30.34

The standard cocktail party lasts three hours and Chavez hires one worker for every six guests, so that works out to one-half hour of labor per guest. These workers are hired only as needed and are paid only for the hours they actually work.

When bidding on cocktail parties, Chavez adds a 12% markup to yield a price of about $39 per guest. She is confident about her estimates of the costs of food and beverages and labor but is not as comfortable with the estimate of overhead cost. The $18.68 overhead cost per labor-hour was determined by dividing total overhead expenses for the last 12 months by total labor-hours for the same period. Monthly data concerning overhead costs and labor-hours follow:

Month	Labor-Hours			Overhead Expenses
January	2,900			$	49,000
February	2,300				53,000
March	2,500				54,000
April	3,700				58,000
May	4,000				61,000
June	5,000				65,000
July	6,000				68,000
August	7,000				71,000
September	6,500				69,000
October	4,000				62,000
November	3,600				58,000
December	6,000				66,000
Total	53,500			$	734,000

Chavez has received a request to bid on a 195-guest fundraising cocktail party to be given next month by an important local charity. (The party would last the usual three hours.) She would like to win this contract because the guest list for this charity event includes many prominent individuals that she would like to secure as future clients. Maria is confident that these potential customers would be favorably impressed by her company’s services at the charity event.

2a. Use the least-squares regression method to estimate the fixed and variable components of overhead expenses. (Round the Variable cost to 2 decimal places and Fixed Cost to the nearest whole dollar amount.)

2b. Express these estimates in the form Y = a + bX. (Round the Variable cost to 2 decimal places and Fixed Cost to the nearest whole dollar amount.)

Answer 1

2.a.
Unit variable cost = b =	(12*3388900000-53500*734000) / (12*266850000 - (53500)^2)
=	(40666800000 - 39269000000) / (3202200000 - 2862250000)
=	1397800000 / 339950000
=	$4.11
Total fixed costs = a    =	(734000 - 4.11*53500) / 12
=	514115 / 12
=	$42,843
Month	Labor	Overhead
	Hours	Expenses
	x	y	x^2	x*y
January	2900	49000	8410000	142100000
February	2300	53000	5290000	121900000
March	2500	54000	6250000	135000000
April	3700	58000	13690000	214600000
May	4000	61000	16000000	244000000
June	5000	65000	25000000	325000000
July	6000	68000	36000000	408000000
August	7000	71000	49000000	497000000
September	6500	69000	42250000	448500000
October	4000	62000	16000000	248000000
November	3600	58000	12960000	208800000
December	6000	66000	36000000	396000000
	53500	734000	266850000	3388900000
	Σx	Σy	Σx2	Σxy
Formulas
Unit Variable Cost=b=(nΣxy-Σx.Σy) / ((nΣx^2-(Σx)^2)
Total Fixed Cost=a=(Σy-bΣx) / n
Where,
n is number of pairs of units—total-cost used in the calculation;
Σy is the sum of total costs of all data pairs;
Σx is the sum of units of all data pairs;
Σxy is the sum of the products of cost and units of all data pairs; and
Σx2 is the sum of squares of units of all data pairs.
2.b.
The linear regression model is represented by
Total cost Y = 42,843 + 4.11 x
Where x is the number of labor hours.