Ralph Manufacturing uses an activity$-$based costing. The company produces $24,000$ units of Model X and

$30,000$ units of Model Y$.$ Information relating to the two products is as follows.

Costs Activity Drivers Model X Model Y

Materials Handling $$40,000$ Number of moves $4,0006,000$

Labor$-$related Overhead $$120,000$ Direct labor hours $8,00012,000$

Setting up $$60,000$ Number of setups $5,0007,000$

Product Design $$100,000$ Number of designs $812$

Inspecting $$120,000$ Inspection batches $10,00014,000$

Purchasing $$70,000$ Number of purchase orders $3040$

$(1)$ Compute the assigned costs for X and Y under the traditional ABC.

$(2)$ Compute the assigned costs for X and Y using the two most expensive activities under the

approximately relevant ABC.

$(3)$ Using ABC as a benchmark, calculate the percentage error and comment on the accuracy of the

reduced system.