   # spring garden tool formula

Topics: Optimization / Pages: 2 (344 words) / Published: Feb 16th, 2014
COMM3411 Assignment Spring Garden Tools Formula Sheet Decision Variables:
This problem contains 20 decision variables, representing the number of production of each type of tools produce in different stages.
Let
i = t (Trowel)
= h (Hoe)
= r (Rake)
= s (Shovel)
Then
R1i = regular production of product i in stage 1 S1i = subcontracted production of product i in stage 1 O1i = overtime production of product i in stage 1 R2i = regular production of product i in stage 2 O2i = overtime production of product i in stage 2

The 20 variables are in follow:
1. R1t = regular production of Trowel in stage 1
2. R1h = regular production of Hoe in stage 1
3. R1r = regular production of Rake in stage 1
4. R1s = regular production of Shovel in stage 1
5. S1t = subcontracted production of Trowel in stage 1
6. S1h = subcontracted production of Hoe in stage 1
7. S1r = subcontracted production of Rake in stage 1
8. S1s = subcontracted production of Shovel in stage 1
9. O1t = overtime production of Trowel in stage 1
10. O1h = overtime production of Hoe in stage 1
11. O1r = overtime production of Rake in stage 1
12. O1s = overtime production of Shovel in stage 1
13. R2t = regular production of Trowel in stage 2
14. R2h = regular production of Hoe in stage 2
15. R2r = regular production of Rake in stage 2
16. R2s = regular production of Shovel in stage 2
17. O2t = overtime production of Trowel in stage 2
18. O2h = overtime production of Hoe in stage 2
19. O2r = overtime production of Rake in stage 2
20. O2s = overtime production of Shovel in stage 2

The objective function
The Springs Company’s objective is to minimize total production cost.

Minimize Z = \$6R1t + 10R1h + 8R1r + 10R1s + 7.2S1t + 12S1h + 9.6S1r + 12S1s + 6.2O1t +10.7O1h + 8.5O1r + 10.7O1s + 3R2t +5R2h + 4R2r + 5R2s + 3.1O2t + 5.4O2h + 4.3O2r +5.4O2s

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