Question:

A chicken farmer has 1000 chickens that cost $0.50 per chicken per week to rear at the start of each week. On the last day of every week, he sells exactly k chickens, where k is a positive integer and 1000 is divisible by k, to a restaurant. In the first week, the price of each chicken is $ 12. After each week, the price of the remaining chickens drops by 5 % the existing price. The sale continues until the farmer has sold all of his 1000 chickens.

Show that, when he has sold all his chickens, the total cost of rearing the chickens is $ (250/k)(1000 + k)

# There are actually 2 parts to the question, but I would like to try the second part myself...so please help me with the first part. Thank you very much!