Homework SourseMaria Chavez owns a catering company that serves food and be
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:
Labor (0.5 hour @ $10.00
/hr.)
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:
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.)
| 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 |
Solution
November
| 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 | |||
| x | y | x2 | xy | |||
| Formulas | ||||||
| Unit Variable Cost=b=(nxy-x.y) / ((nx^2-(x)^2) | ||||||
| Total Fixed Cost=a=(y-bx) / n | ||||||
| Where, | ||||||
| n is number of pairs of units—total-cost used in the calculation; | ||||||
| y is the sum of total costs of all data pairs; | ||||||
| x is the sum of units of all data pairs; | ||||||
| xy is the sum of the products of cost and units of all data pairs; and | ||||||
| x2 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. | ||||||
