Rose Hill, a soybean farm in northern Minnesota, has a herd of $33$ dairy cows. The cows produce approximately $1,820$ gallons of milk per week. The farm currently sells all its milk to a nearby processor for $$1\mathrm{.}25$ per gallon, a significant drop from the $$2\mathrm{.}00$ per gallon they were able to charge five years ago. It costs $$1\mathrm{.}60$ per gallon to produce the milk.

The owners of Rose Hill are deciding whether to sell the dairy cows or expand into the artisan cheese market. Both owners have prior cheese$-$making experience and they already have all the needed equipment.

It takes $0\mathrm{.}8$ gallons of milk to make a pound of cheese. Costs to produce a pound of cheese are expected to total $$7$ per pound. Artisan cheeses are currently selling for $$10$ per pound at farmer$$s markets and upscale groceries.

Required

a$.$ How much incremental profit would Rose Hill recognize if half the milk each week was used to make cheese?

b$.$ How much, in total, would Rose Hill earn each week if half the milk was used to make cheese and half was sold to the processor?

c$.$ How much of the milk would need to be used to make cheese each week in order for Rose Hill to break even on its dairy operations assuming no cows were sold? $($Note: Any milk not used to make cheese would still be sold to a processor.$)$

Note: Do not round your answers.

gallons of milk used to make cheese:$\_\_\_\_\_\_$

gallons of milk sold to a processor:$\_\_\_\_\_\_\_\_$