Problem $4(11$ points$)$

Kombucha Crafters, Inc." The company is evaluating its production processes in anticipation of a significant increase in demand due to a new partnership with a national health food store chain. The owner, Alex Rivera, is considering three different production processes to meet this demand: Small$-$Batch Brewing $($SBB$),$ Automated Fermentation System $($AFS$),$ and Advanced Bottling Line $($ABL$).$ Each process has different cost structures, primarily due to the varying levels of automation and scalability.

Cost Structures for Each Process

Small$-$Batch Brewing $($SBB$)$

Annual contracted units: $50,000$ bottles

Annual fixed cost: $$30,000$

Per unit variable cost: $$2\mathrm{.}00$

Automated Fermentation System $($AFS$)$

Annual contracted units: $50,000$ bottles

Annual fixed cost: $$70,000$

Per unit variable cost: $$1\mathrm{.}50$

Advanced Bottling Line $($ABL$)$

Annual contracted units: $50,000$ bottles

Annual fixed cost: $$120,000$

Per unit variable cost: $$1\mathrm{.}00$

$5$ points$)$ Calculate the crossover points between the three processes. Show all work.