The Acme Manufacturing Company is concerned about its warehouse needs and how they can best be met. The company produces a line of spare parts for appliance. Due to the combination of production policies and demand patterns, warehousing space requirement 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. 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 $33,750,000$

Warehouse inventory turns at the rate of two times per month. The price of merchandise is $$5$ per lb$.$ On average, merchandise occupies $0\mathrm{.}8$ cubic feet of warehouse space per lb and can be stacked $10$ ft$.$ high. Given aisles, administrative space, and normal operating efficiency, only $60$ percent of the total warehouse is actually used for storage.

A private warehouse can be constructed and equipped for $$45$ per sq$.$ ft$.$ and can be amortized over $25$ years. The cost of operations is $$0\mathrm{.}05$ per lb of throughput. Annual fixed costs amount to $$15$ per sq$.$ ft$.$ of total space. Space may also be rented for a storage charge on inventory of $$0\mathrm{.}07$ per lb per month and a handling charge of $$0\mathrm{.}07$ per lb of throughput.

Suppose the company is struggling about building a large $(64,000$ sq$.$ ft$),$ median $(32,000$ sq$.$ ft$),$ or small $(16,000$ sq$.$ ft$)$ warehouse. What size of private warehouse should be constructed? What amount of public warehouse space should be rented?