Question 4: EOQ with Finite Production Rate (20 points)

A bicycle production company receives a demand for 15,000 bikes each year, and needs to produce one frame for each bike. The production setup cost for the company is $500, and per unit production cost is $10. The company can produce 1,500 frames per month. (There are 12 months in one year.) The yearly interest rate is estimated to be 30%.

a. [10 points] What is the optimal production quantity for frames and maximum inventory level that can be achieved in any order cycle?

b. [5 points] What is the annual total cost of setup, ordering, and inventory holding?

c. [5 points] Suppose that the warehouse for the frames has a capacity for 3,000 frames only. Would this warehouse capacity restriction change the decision of the company made in Part (a)? Why?