Bill Hide, managing partner of the law firm Hide & Associ-ates, is examining how secretarial support costs behave with changes in monthly professional labor- hours billed to clients. Assume the following historical data:

Total Secretarial Support Costs Professional Labor- Hours Billed to Clients

$ 35,000.................2,000

38,000................. 3,000

39,500 .................4,000

49,000 .................5,000

52,000 .................6,500

58,000 .................7,500

Required

1. Compute the linear cost function, relating total secretarial support costs to professional labor- hours, using the representative observations of 3,000 and 6,500 hours. Plot the linear cost function. Does the constant component of the cost function represent the fixed secretarial support costs of Hide & Associates? Why?

2. What would be the predicted total overhead costs for (a) 4,000 hours and (b) 7,500 hours using the cost function estimated in requirement 1? Plot the predicted costs and actual costs for 4,000 and 7,500 hours.

3. Hide had a chance to accept a special job that would have boosted professional labor- hours from 3,000 to 4,000 hours. Suppose Hide, guided by the linear cost function, rejected this job because it would have brought a total increase in contribution margin (sales minus all variable costs) of $ 3,200, before deducting the predicted increase in total overhead cost, $ 4,000. What is the actual effect of this decision on overall firm income?