Can you show work and all steps

Problem $3.($Chapter $12$: Storage and Handling Decisions, hint: similar to the sizing problem example in class, see Module $3$ Ch$12$ Part $1$ on Canvas$)$ 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 kniown 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 $0\mathrm{.}1$ cubic feet of warehouse space and can be stacked $10ft.$ 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\mathrm{.}04$ per $1lb$ 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\mathrm{.}06$ per $lb$ per month and a handling charge of $$0\mathrm{.}05$ per $lb$ of throughput. Monthly sales rates for a typical year are as follows:

$\backslash$table$[[$Month$,$Sales $($$$)],[$Jan$.,5,000,000$