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 to home improvement discount chains. The Spring Company's four most popular small garden tools are a trowel, a pickaxe, 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 comprises two stages. The first stage includes two operations: stamping out the metal tool heads and drilling holes in them. The completed tool heads then flow into 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 processing times per tool for each operation are provided in Table 1.

The steel the company uses is ordered from an iron and steel works in Japan. The company has 10,000 square feet of steel available each month. The metal required for each tool and the monthly contracted production volume per tool are provided in Table 2.

The primary reason the company has survived and prospered are its ability to always 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 since 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. The Spring Company may subcontract the whole tool head manufacturing process (stage 1, involving the operations of stamping and drilling together) for any number of tools. However, the company does have 100 hours of overtime available each month for each operation regardless of stage. The regular production and overtime costs per tool for all operations in both stages are provided in Table 3. 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 operation and for the number of tool heads subcontracted, at the minimum cost.

Answer the following question independent of one another, based on the GAMS solution and sensitivity report and without solving a new problem:

(a) Another 10 hours of (regular) work every month become available. Which operation would you devote them to and why?

(b) A sudden problem in the iron and steel works in Japan causes a shortage of 200 ft² of steel for a month only. What will the cost of production be during that month?

(c) Find the cost of production under each of the following changes to individual tool production costs, independent of one another.

i. The regular cost of packaging one pickaxe becomes $5.20, without affecting the subcontracting cost.

ii. The overtime cost of finishing one rake becomes $4.10.

iii. The regular cost of stamping one trowel becomes $5.00, without affecting the subcontracting cost.

Table 1: Processing Times per Tool & Time Availability Operation Stamping Drilling Assembly Finishing Packaging Tool (hr/unit) Total Hours Trowel Pickaxe Rake Shovel Available per Month 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 0.02 0.10 550 0.03 0.15 0.04 0.15 500 0.21 Table 2: Metal Requirement & Contracted Sales Trowel Pickaxe Rake Shovel Sheet Metal 1.2 1.6 2.1 2.4 Monthly Contracted Sales 1,800 1,400 1,600 1,800 Table 3: Cost of Production per Tool Trowel Pickaxe Rake Shovel Stage 1 Regular Cost ($) Overtime Cost ($) 6.00 6.20 10.00 10.70 8.00 8.50 10.00 10.70 Stage 3 Regular Cost ($) Overtime Cost ($). 3.00 3.10 5.00 5.40 4.00 4.30 5.00 5.40 Table 1: Processing Times per Tool & Time Availability Operation Stamping Drilling Assembly Finishing Packaging Tool (hr/unit) Total Hours Trowel Pickaxe Rake Shovel Available per Month 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 0.02 0.10 550 0.03 0.15 0.04 0.15 500 0.21 Table 2: Metal Requirement & Contracted Sales Trowel Pickaxe Rake Shovel Sheet Metal 1.2 1.6 2.1 2.4 Monthly Contracted Sales 1,800 1,400 1,600 1,800 Table 3: Cost of Production per Tool Trowel Pickaxe Rake Shovel Stage 1 Regular Cost ($) Overtime Cost ($) 6.00 6.20 10.00 10.70 8.00 8.50 10.00 10.70 Stage 3 Regular Cost ($) Overtime Cost ($). 3.00 3.10 5.00 5.40 4.00 4.30 5.00 5.40