Better Gardens Sdn. Bhd. has a factory manufacturing garden tools in Shah Alam.
ID: 3142494 • Letter: B
Question
Better Gardens Sdn. Bhd. has a factory manufacturing garden tools in Shah Alam. The company sells its garden tools to distributors as well as directly to hardware stores and DIY outlets in the whole of Klang Valley. The six most popular small garden tools which the company manufactures are digging forks, hand trowels, hoes, rakes, spades, and shovels. Each of these tools is made from durable steel and has a wooden handle. The manufacturing process of these tools goes through 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 proceed 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: The company has 1, 200 square meters of sheet steel available each month. The unit price and the metal required for each tool and the monthly contracted sales are provided in the following table: The company's director wishes to ensure that the monthly sales demand is met on time and he uses scientific techniques to run his business. As a result, he is willing to use overtime production in order to meet its sales requirements, and the company also has an arrangement with a local tool and the company to manufacture the tool heads if needed. The company feels comfortable subcontracting the first stage operations because it is easier to detect defects prior to assembly and finishing. However, the company does have 150 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. The cost of subcontracting in stage 1 adds 30% to the regular production cost. The company wants to establish a production schedule for regular and overtime production in each stage and for the number of tool heads subcontracted, to maximize its monthly profit. (a) Formulate a complete linear programming model in algebraic form that shows the individual constraints and decision variables for this problem. (b) Formulate this same model on an Excel spreadsheet. Then use the Excel Solver to solve the model. (c) Based on your solution in part (b) what are the most critical resources in the production process? (d) Using the sensitivity report produced in your Excel solution, discuss the implications if there are changes in the critical resources identified in part (c).Explanation / Answer
Ans-
Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).
1. They grow 12 different varieties.
2. Everybody grows exactly 4 different varieties
3. Each variety is at least in one garden.
4. Only one variety is in 4 gardens.
5. Only in one garden are all 3 kinds of crops.
6. Only in one garden are all 4 varieties of one kind of crops.
7. Pear is only in the two border gardens.
8. Paul's garden is in the middle with no lily.
9. Aster grower doesn't grow vegetables.
10. Rose growers don't grow parsley.
11. Nuts grower has also gourd and parsley.
12. In the first garden are apples and cherries.
13. Only in two gardens are cherries.
14. Sam has onions and cherries.
15. Luke grows exactly two kinds of fruit.
16. Tulip is only in two gardens.
17. Apple is in a single garden.
18. Only in one garden next to Zick's is parsley.
19. Sam's garden is not on the border.
20. Hank grows neither vegetables nor asters.
21. Paul has exactly three kinds of vegetable.
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