Emma's Precision Tooling has a contract for $120,000$ units of a specialized component. Emma Thompson, the owner, has evaluated three different production process alternatives. The fixed costs for each process are as follows: for Standard Machinery $($SM$),$ $$250,000$; for Automated Cell System $($ACS$),$ $$500,000$; and for Full Robotic System $($FRS$),$ $$900,000.$ The variable costs per unit are: SM$,$ $$14$; ACS, $$11$; and FRS$,$ $$7.$

a$.$ Calculate the total cost for each process alternative if the production is set at $120,000$ units. Which process should Emma choose?

b$.$ Find the crossover points for these processes. Determine the range of units you would make using each process

c$.$ Determine which process should be selected if the production volume is $220,000$ units.