Chapter 10, Problem 10.29E

Linear cost approximation. Dr. Young, of Young and Associates, LLP, is examining how overhead costs behave as a function of monthly physician contact hours billed to patients. The historical data are as follows:

Total Overhead Costs	Physician Contact Hours Billed to Patients
$ 90,000	150
105,000	200
111,000	250
125,000	300
137,000	350
150,000	400

1. 1. Compute the linear cost function, relating total overhead costs to physician contact hours, using the representative observations of 200 and 300 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of Young and Associates? Why?

    Required

1. 2. What would be the predicted total overhead costs for (a) 150 hours and (b) 400 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 150 and 400 hours.
2. 3. Dr. Young had a chance to do some school physicals that would have boosted physician contact hours billed to patients from 200 to 250 hours. Suppose Dr. Young, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of $9,000, before deducting the predicted increase in total overhead cost, $10,000. What is the total contribution margin actually forgone?