Lakey Corporation has an activity$-$based costing system with three actlvity cost pools$--$Machining, Setting Up$,$ and Other. The company's overhead costs have already been allocated to the cost pools and total $$11,000$ for the Machining cost pool, $$26,200$ for the Setting Up cost pool, and $$9,800$ for the Other cost pool. Costs in the Machining cost pool are assigned to products based on machine$-$hours $($MHs$)$ and costs in the Setting Up cost pool are assigned to products based on the number of batches. Costs in the Other cost pool are not assigned to products. Data concerning the two products appear below:

$\backslash$table$[[,$MHS$,$Batches$],[$Product S$7,8,400,200],[$Product W$3,1,600,1,800],[$Total$,10,000,2,000]]$

Required:

a$.$ Calculate activity rates for each activity cost pool using activity$-$based costing.

b$.$ Determine the amount of overhead cost that would be assigned to each product using activity$-$based costing.