John Smith owns a catering company that prepares food and beverages for banquets and parties. For a standard party the cost on a per-person basis is as follows:

Food and beverages	$20.00
Labor (0.5 hour @ $8 per hour)	4.00
Overhead (0.5 hour @ $12 per hour)..	6.00
Total cost per person...	$30.00

Smith is quite certain about his estimate of the food, beverages, and labor costs, but is not as comfortable with the overhead estimate. The overhead estimate was based on actual data for the past 12 months, which are presented here. These data indicate that overhead costs vary with the direct labor hours used. The $12 estimate was determined by dividing total overhead costs for the 12 months by total labor-hours.

Month	Labor-Hours	Actual overhead costs
1	2,500	$40,000
2	2,700	35,000
3	3,000	39,000
4	4,200	54,000
5	5,000	60,000
6	5,500	64,000
7	6,500	70,000
8	4,500	57,000
9	7,000	75,000
10	4,500	58,000
11	3,100	32,000
12	6,500	76,000
Total	55,000	660,000

Required:

1. Estimate a linear cost function with overhead costs as the dependent variable and the labor-hours as the independent variable. Write the equation for the linear cost function as: y = a + (b X)

2. This question asks you to interpret the coefficients of your linear cost function in (1):
   1. What does a represent in relation to y?
   2. What does b represent in relation to y?
   3. What does X represent?

3. Plot the relationship between overhead costs and labor-hours.

4. Evaluate your linear cost function using these criteria (see Exhibit 10-18):
   1. Economic plausibility
   2. Goodness of fit
   3. Slope of the linear cost function
5. As indicated above, the overhead cost of $12 per hour (or $6 per person) was determined by dividing total overhead costs for the 12 months by total labor-hours. Do you agree with this approach? Why or why not? Be specific.

6. Using the results from your linear cost function, what is the variable cost per person for a standard party? Show your calculations and make sure that all your numbers are labeled.

7. John Smith has been asked to prepare a bid for a 200-person standard party to be given next month. Determine the minimum bid price that Smith would be willing to submit to recoup variable costs. Assume that, except for the first year, the catering business has reported profits every year. Show your calculations and make sure that all your numbers are labeled.