Dot's Restaurant must decide between two technology processes in their kitchen. They only serve dinner after $4$ p$.$m$.$ on a small island called Sanibel. The restaurant is open $250$ days per year. Dot and her husband, Ham, are retired. They became bored playing golf five times a week and decided to open this boutique restaurant. Process A uses an induction oven and microwave process with a fixed cost of $$48,000$ and a variable cost of $$4\mathrm{.}17$ per meal. Process B uses a gas fired oven process with heating lamps with a fixed cost of $$20,000$ and a variable cost of $$5\mathrm{.}53$ per meal. Process A speeds up cooking and delivery time. The average selling price per meal is $$31\mathrm{.}16.$

a$.$ What is the break$-$even quantity? Round your answer to the nearest whole number. meals

b$.$ If the restaurant manager expects to sell $8,000$ meals, which option, $A$ or $B,$ is best? Round your answers the nearest dollar.

Cost of Option A: $

Cost of Option B: $

So$,$ is the best option.

c$.$ Is the restaurant profitable if they purchase the process option you recommend in part $($b$)?$ Enter your answer as a positive value. Round your answer to the nearest dollar.

The restaurant's is $