Assume Cassin Co manufactures only two products $-15,000$ units of Product A and $9,000$ units of Product B$.$ It is considering implementing an activity$-$based costing $($ABC$)$ system that allocates all of its manufacturing overhead to three cost pools. The following additional information is available for the company as a whole and for Products A and $B$ :

$\backslash$table$[[$Activity Cost Pool,Activity Measure,Estimated Overhead Cost,Expected Activity,$],[$Machining$,$Machine$-$hours,$$330,000,18,325,$MH$],[$Machine setups,Number of setups,$$180,000,200,$Setups$],[$Product design,Number of products,$$91,000,2,$Products$]]$

$\backslash$table$[[$Activity Measure,Product A$,$Product B$],[$Machine$-$hours,$7,000,6,000],[$Number of setups,$70,160],[$Number of products,$1,1]]$

Using the ABC system, how much total overhead cost would Cassin Co assign from all of the activities to Product A$?($rounded to nearest dollar$)$

A $$187,646$

$$260,359$

$$ $$234,557$

$$ $$340,108$