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II. 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 tool heads and drilling screw holes in them. The completed tool heads then flow to the second stage, which includes an assembly operation where the handles are attached to the tool 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 Available per Month Operation Trowel Hoe Rake Shovel Stamping Drilling Assembly Finishing Packaging 0.04 0.17 0.06 0.12 500 0.05 0.14 0.14 400 0.06 0.13 0.05 0.10 600 0.05 0.21 0.02 0.10 550 0.03 0.15 0.04 0.15 500 The steel the 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: Sheet Metal (ft.) 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 overtime 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

II. 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 tool heads and drilling screw holes in them. The completed tool heads then flow to the second stage, which includes an assembly operation where the handles are attached to the tool 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 Available per Month Operation Trowel Hoe Rake Shovel Stamping Drilling Assembly Finishing Packaging 0.04 0.17 0.06 0.12 500 0.05 0.14 0.14 400 0.06 0.13 0.05 0.10 600 0.05 0.21 0.02 0.10 550 0.03 0.15 0.04 0.15 500 The steel the 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: Sheet Metal (ft.) 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 overtime 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

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Can someone help me 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?

II. 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 tool heads and drilling screw holes in them. The completed tool heads then flow to the second stage, which includes an assembly operation where the handles are attached to the tool 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 Available per Month Operation Trowel Hoe Rake Shovel 0.04 0.17 0.12 Stamping Drilling Assembly Finishing Packaging 0.06 500 0.05 0.14 0.14 400 0.06 0.13 0.05 0.10 600 0.05 0.21 0.02 0.10 550 0.03 0.15 0.04 0.15 500 The steel the 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: Sheet Metal (ft.) Monthly Contracted Sales Trowel 1.2 1,800 1,400 1,600 Hoe 1.6 Rake 2.1 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 overtime 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
Transcribed Image Text:II. 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 tool heads and drilling screw holes in them. The completed tool heads then flow to the second stage, which includes an assembly operation where the handles are attached to the tool 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 Available per Month Operation Trowel Hoe Rake Shovel 0.04 0.17 0.12 Stamping Drilling Assembly Finishing Packaging 0.06 500 0.05 0.14 0.14 400 0.06 0.13 0.05 0.10 600 0.05 0.21 0.02 0.10 550 0.03 0.15 0.04 0.15 500 The steel the 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: Sheet Metal (ft.) Monthly Contracted Sales Trowel 1.2 1,800 1,400 1,600 Hoe 1.6 Rake 2.1 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 overtime 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 was 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 Cost Overtime Cost Cost Cost Trowel $6.00 S6.20 S3.00 $3.10 5.40 Hoe 10.00 10.70 5.00 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 fost. 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?
Transcribed Image Text: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 was 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 Cost Overtime Cost Cost Cost Trowel $6.00 S6.20 S3.00 $3.10 5.40 Hoe 10.00 10.70 5.00 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 fost. 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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