Spring Garden Tools -Linear Programming: Modeling Examples

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Introduction to Management Science (Decision Support Systems) Spring Garden Tools- linear programming model -Excel solution only. The book that this came from is Introduction to Management Science Ninth Edition, Bernard W. Taylor III. You have to show the problem analysis, model development, and their use of appropriate software to solve the problem.

Spring Garden Tools.

The Spring family has owned and operated a garden tool and implements manufacturing company since 1952. The company sells garden tools to distributors and also directly to hardware stores and home improvement discount chains. The Spring company’s four most popular small garden tools are a trowel,a hoe,a rake,and a shovel. Each of these tools is made from durable steel and has a wooden handle. The Spring family prides itself on its high-quality tools.
The manufacturing process encompasses two stages. The first stage includes two operations – stamping out the metal tools heads and drilling screw holes in them. The completed tools heads then flow to the second stage, which includes an assembly operation where the handles are attached to the tools heads, a finishing step, and packaging. The processing times per tool for each operation are provided in the following table:

Tool (Hr/Unit)
Total Hours
Operation Trowel Hoe Rake Shovel Available per month
Stamping 0.04 0.17 0.06 0.12 500
Drilling 0.05 0.14 – 0.14 400
Assembly 0.06 0.13 0.05 0.10 600
Finishing 0.05 0.21 0.02 0.10 550
Packaging 0.03 0.15 0.04 0.15 500

The steel company uses is ordered from an iron and steel works in Japan.
The company has 10,000 square feet of sheet steel available each month. The metal required for each tool and the monthly contracted production volume per tool are provided in the following table:

Steel Metal (ft.2) Monthly Contracted Sales
Trowel 1.2 1,800
Hoe 1.6 1,400
Rake 2.1 1,600
Shovel 2.4 1,800

The primary reasons the company has survived and prospered are its ability always to meet customer demand on time and its high quality. As a result, the Spring Company will produce on an over-time basis in order to meet its sales requirements, and it also has a long-standing arrangement with a local tool and die company to manufacture its tool heads. The Spring Company feels comfortable subcontracting the first-stage operations because it is easier to detect defects prior to assembly and finishing. For the same reason, the company will not subcontract for the entire tool because defects would be particularly hard to detect after the tool is finished and packaged. However, the company does have 100 hours of overtime available each month for each operation in both stages. The regular production and overtime costs per tool for both stages are provided in the following table:

Stage 1 Stage 2
Regular Overtime Regular Overtime
Cost Cost Cost Cost
Trowel $6.00 $6.20 $3.00 $3.10
Hoe $10.00 $10.70 $5.00 $5.40
Rake $8.00 $8.50 $4.00 $4.30
Shovel $10.00 $10.70 $5.00 $5.40

The cost of subcontracting in stage 1 adds 20% to the regular production cost.
The Spring Company wants to establish a production schedule for regular and overtime production in each stage and for the number of tool heads subcontracted, at the minimum cost. Formulate a linear programming model for this problem and solve the model using the computer. Which resources appear to be most critical in the production process?

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