The Acme Manufacturing Company is concerned about its warehouse needs and how they can be best met. The company produces a line of spare parts for appliances.

Due to the combination of production policies and demand patterns, warehousing space requirements vary considerably throughout the year. Space requirements are known with a great deal of certainty because the product line satisfies a replacement market. Growth, or
decline, in production and sales is not anticipated in the near future. Warehouse inventory turns at the rate of two times per month. A dollar's worth of merchandise occupies 0.1 cubic feet of warehouse space and can be stacked 10 ft. high. The product density is $5 per lb.

Given aisles, administrative space, and normal operating efficiency, only 40 percent of the total warehouse space is actually used for storage. A private warehouse can be constructed and equipped for $35 per sq. ft. and can be amortized over 20 years. The cost of operation is $0.04 per lb of throughput. Annual fixed costs amount to $10 per sq. ft. of total space. Space may also be rented for a storage charge on inventory of $0.06 per lb per month and a handling charge of $0.05 per lb of throughput.

Monthly sales rates for a typical year are as follows:
Month Sales ($)
Jan. 5,000,000
Feb. 4,000,000
Mar. 3,000,000
Apr. 2,000,000
May 1,000,000
June 250,000
July 1,250,000
Aug. 2,250,000
Sept. 3,000,000
Oct. 3,500,000
Nov. 4,000,000
Dec. 4,500,000
Total 33,750,000

Consider the following two options:

(1) Construct a 10,000 sq. ft. of private warehouse and rent public warehouse as needed.

(2) Do not construct a private warehouse, and use only public warehouse. What are the annual costs for each option, and which one has a lower annual cost?