(Show all your works: including all computational procedures and details)

(AEC) supplies computer part to computer manufacturers. Demand for the computer parts is 10,000 (R) per month. To exploit economies of scale, AEC produces a production batch size of Q and incurred a flat production setup cost of $1,500 (S). In addition, AEC believes that it cost 20% per year of parts cost to hold it in inventory.

(a) AEC would like to determine the optimal production batch size. What batch size would you recommend for AEC if the cost of producing a computer part is $40 (C)?