Two manufacturing processes are being considered for making a new product. Process #$1$ is less capital intensive, with fixed costs of $$50,000$ per year and variable costs of $$700$ per unit. Process #$2$ has fixed costs of $$400,000$ annually, with variable costs of $$200$ per unit.

What is the break$-$even quantity for the two processes?

If annual sales are expected to be $600$ units, which process should be selected?

If lowest overall costs per year is your overall objective, for what range of annual production quantities should you select Process #$1?$ Process #$2?$

Operations and Engineering have found a way to reduce the cost of Process #$2,$ such that the fixed costs for this process decrease from $$400,000$ to $$300,000$ annually. All other costs remain the same $($Process #$1$ fixed $=$ $$50,000/$ year, Process #$1$ variable $=$ $$700/$ unit, Process #$2$ variable $=$ $$200/$ unit$).$ What is the new break even quantity between the two processes?

Does this change the process selection for the annual sales volume of $600$ units? If so$,$ for what range of annual production quantities should you select Process #$1$ and Process #$2?$