Linear cost approximation. Terry Lawler, managing director of the Little Rock Reviewers Company, is examining how overhead costs behave with changes in monthly professional labor-hours billed to clients. Assume the following historical data:

Total Overhead Costs Professional Labor-Hours Billed to Clients
$330,000 3000
395,000 4000
425,000 5000
467,000 6000
521,000 7500
577,000 8500

a. Compute the linear cost function, relating total overhead costs to professional labor-hours, using the representative observations of 4,000 and 7,500 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed overhead costs of the Little Rock Reviewers Company? Why?
b. What would be the predicted total overhead costs for (a) 5,000 hours and (b) 8,500 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 5,000 and 8,500 hours.
c. Lawler had a chance to accept a special job that would have boosted professional labor-hours from 4,000 to 5,000 hours. Suppose Lawler, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin of S31,OOO, before deducting the predicted increase in total overhead cost, $36,000. What is the total contribution margin actually forgone?