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 0.1 cubic feet of warehouse space per lb and can be stacked 10 ft. high. Given aisles, administrative space, and normal operating efficiency, only 50 percent of the total warehouse is actually used for storage. A private warehouse can be constructed and equipped for $40 per sq. ft. and can be amortized over 20 years. The cost of operations is $0.03 per dollar of throughput (lb). Annual fixed costs amount to $15 per sq. ft. of total space. Space may also be rented for a storage charge on inventory of $0.07 per lb per month and a handling charge of $0.06 per lb of throughput. Suppose the company is struggling about building a large (50,000 sq. ft), median (35,000 sq. ft), or small (15,000 sq. ft) warehouse. What size of private warehouse should be constructed? What amount of public warehouse space should be rented?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...

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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 0.1 cubic feet of warehouse space per lb and can be stacked 10 ft. high. Given aisles, administrative space, and normal operating efficiency, only 50 percent of the total warehouse is actually used for storage. A private warehouse can be constructed and equipped for $40 per sq. ft. and can be amortized over 20 years. The cost of operations is $0.03 per dollar of throughput (lb). Annual fixed costs amount to $15 per sq. ft. of total space. Space may also be rented for a storage charge on inventory of $0.07 per lb per month and a handling charge of $0.06 per lb of throughput. Suppose the company is struggling about building a large (50,000 sq. ft), median (35,000 sq. ft), or small (15,000 sq. ft) warehouse. What size of private warehouse should be constructed? What amount of public warehouse space should be rented?

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