10-24 Linear cost approximation. Terry Lawler, managing director of the Memphis Consulting Group, is

examining how overhead costs behave with changes in monthly professional labor-hours billed to clients.

Assume the following historical data:

Professional Labor-Hours

Total Overhead Costs Billed to Clients

$340,000 3,000

400,000 4,000

435,000 5,000

477,000 6,000

529,000 7,000

587,000 8,000

required:

1. Compute the linear cost function, relating total overhead cost to professional labor-hours, using the representative

observations of 4,000 and 7,000 hours. Plot the linear cost function. Does the constant component

of the cost function represent the fixed overhead costs of the Memphis Consulting Group? Why?

2. What would be the predicted total overhead costs for (a) 5,000 hours and (b) 8,000 hours using the cost

function estimated in requirement 1? Plot the predicted costs and actual costs for 5,000 and 8,000 hours.

3. 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 $38,000, before deducting the predicted

increase in total overhead cost, $43,000. What is the total contribution margin actually forgone?