Zan Azlett and Angela Zesiger have joined forces to start A&Z Lettuce Products, a processor of packaged shredded lettuce for institutional use. Zan has years of food processing experience, and Angela has extensive commercial food preparation experience. The process will consist of opening crates of lettuce and then sorting, washing, slicing, preserving, and finally packaging the prepared lettuce. Together, with help from vendors, they think they can adequately estimate demand, fixed costs, revenues, and variable cost per bag of lettuce. They think a largely manual process will have monthly fixed costs of $$40,000$ and variable costs of $$1\mathrm{.}60$ per bag. A more mechanized process will have fixed costs of $$72,000$ per month with variable costs of $$1\mathrm{.}25$ per bag. They expect to sell the shredded lettuce for $$3\mathrm{.}00$ per bag.

a$)$ The break$-$even quantity in units for the manual process $=$ whole number$).$ bags $($round your response to the nearest

b$)$ The revenue for the manual process at the break$-$even quantity $=$$$85713($round your response to the nearest whole number$).$

c$)$ The break$-$even quantity in units for the mechanized process $=41142$ bags $($round your response to the nearest whole number$).$

d$)$ The revenue for the mechanized process at the break$-$even quantity $=$$$123426($round your response to the nearest whole number$).$

e$)$ For monthly sales of $55,000$ bags, for the option with manual processing, A&Z Lettuce Products will have a profit of $ $($round your response to the nearest whole number and include a minus sign if the profit is negative$).$