Please give answer: 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.

$5$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

Feb.

$4$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

Mar.

$3$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

Apr.

$2$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

May

$1$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

June

$2$

$5$

$0$

$,$

$0$

$0$

$0$

July

$1$

$,$

$2$

$5$

$0$

$,$

$0$

$0$

$0$

Aug.

$2$

$,$

$2$

$5$

$0$

$,$

$0$

$0$

$0$

Sept.

$3$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

Oct.

$3$

$,$

$5$

$0$

$0$

$,$

$0$

$0$

$0$

Nov.

$4$

$,$

$0$

$0$

$0$

$,$

$0$

$0$

$0$

Dec.

$4$

$,$

$5$

$0$

$0$

$,$

$0$

$0$

$0$

Total

$3$

$3$

$,$

$7$

$5$

$0$

$,$

$0$

$0$

$0$

Warehouse inventory turns at the rate of two times per month. The price of merchandise is $

$5$

$$per lb

$.$

$$On average, merchandise occupies

$0$

$.$

$8$

$$cubic feet of warehouse space per lb and can be stacked

$1$

$0$

$$ft

$.$

$$high$.$ Given aisles, administrative space, and normal operating efficiency, only

$6$

$0$

$$percent of the total warehouse is actually used for storage.

A private warehouse can be constructed and equipped for $

$4$

$5$

$$per sq

$.$

$$ft

$.$

$$and can be amortized over

$2$

$5$

$$years$.$ The cost of operations is $

$0$

$.$

$0$

$5$

$$per lb of throughput. Annual fixed costs amount to $

$1$

$5$

$$per sq

$.$

$$ft

$.$

$$of total space. Space may also be rented for a storage charge on inventory of $

$0$

$.$

$0$

$7$

$$per lb per month and a handling charge of $

$0$

$.$

$0$

$7$

$$per lb of throughput.

Suppose the company is struggling about building a large

$($

$6$

$4$

$,$

$0$

$0$

$0$

$$sq

$.$

$$ft

$)$

$,$

$$median

$($

$3$

$2$

$,$

$0$

$0$

$0$

$$sq

$.$

$$ft

$)$

$,$

$$or small

$($

$1$

$6$

$,$

$0$

$0$

$0$

$$sq

$.$

$$ft

$)$

$$warehouse$.$ What size of private warehouse should be constructed? What amount of public warehouse space should be rented?