Adobe Reader Touch X Problem 1 Linear Optimization The Spring family has owned and operated a garden tool and implements manufacturing com- pany 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. The second stage includes an assembly operation where the handles are attached to the tool heads, a finishing step, and finally packaging. The pro- cessing 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 0.06 0.2 0.08 0.14 600 Drilling 0.07 0.15 0.02 0.17 450 Assembly 0.08 D.17 0.07 ).14 700 Finishing 0.05 D.21 0.02 0.1 600 Packaging 0.03 0.15 0.04 0.15 550 The steel the company uses is ordered from an iron and steel works in Japan. The company has 15,000 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 Trowe 1.6 2000 Hoe 1600 Rake 2.4 1800 Shovel 2.7 1700 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 sub- contract for the entire tool, because defects would be particularly hard to detect after the tool is finished and packaged. Type here to search O 21:36 ~ DO () ENG 27.12.2020Adobe Reader Touch X However, the company does have 150 hours of overtime available each month for each oper- ation in both stages (not for subcontracted production). 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 8.00 3.30 5.00 5.40 Hoe 12.00 12.50 7.00 7.30 Rake 9.00 9.40 5.00 5.50 Shovel 11.00 11.40 7.00 7.30 The cost of subcontracting in stage 1 adds 10% to the regular production cost. The Spring Company wants to establish a production schedule for regular und overtime pro- duction in each stage and for the number of tool heads subcontracted at the minimum cost. Formulate a linear programming model for this problem. Solve the model using the computer. Document the implementation by screenshots in your PDF-file. Save also the computer software file (e.g. excel on your stick). Interpret the results. Which resources appear to be most critical in the production process? Hint: All garden tools are of course entire products, that's why it is an integer problem. Add a constraint, that these decision variables are integer. Add Constraint X Cell Reference: Constraint: SB$4:SES4 int integer OK Add Cancel Type here to search O 21:36 ~ DO () GENG 27.12.2020
