$2)$ Golden Chicken

Golden Chicken is a wholesale distributor of eggs to local businesses. Under an agreement with its supplier, Golden Chicken can purchase up to $1000$ cases of eggs per day at $$3$ per case. Additional cases beyond $1000$ may be purchased at $$4$ per case. Golden Chicken uses small trucks to deliver the eggs. Each truck can deliver $50$ cases at a cost of $$50$ per route. The current sales of the company are $1000$ cases per day at a wholesale price of $$6$ per case. Calculate the break$-$even quantity for Golden Chicken under the following circumstances:

a$)$ The wholesale price of a case of eggs increases to $$6\mathrm{.}60.$

b$)$ The wholesale price of a case of eggs decreases to $$5\mathrm{.}50.$

c$)$ How would your answer to $($b$)$ change if the current sales level is $800$ cases per day?