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:

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?

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Month Sales ($) Jan. 5,000,000 Feb. 4,000,000 Mar. 3,000,000 Aprг. 2,000,000 May 1,000,000 June 250,000 July 1,250,000 Aug. 2,250,000 Sept. 3,000,000 Oct. 3,500,000 Nov. 4,000,000 Dec. 4,500,000 Total 33,750,000 Month Sales ($) Jan. 5,000,000 Feb. 4,000,000 Mar. 3,000,000 Aprг. 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