Homework Answers
Let X1, X2, X3 be the number of sheds i.e. Shed I, Shed II, Shed III respectively that can be produced from the available hours of Stamping, Painting and Packing.
Equations will be as following:
3X1+X2+3X3 = 1400
2X1+2X2+2X3 = 1200
X1+2X2+4X3 = 1700
| Using Gaussian elimination for 3 by 3 matrices |
| Matrix as following: | ||||||
| 3 | 1 | 3 | 1400 | |||
| A= | 2 | 2 | 2 | B= | 1200 | |
| 1 | 2 | 4 | 1700 | |||
| Normalizing the Matrix | ||||||
| 1 | 0.333333 | 1 | 466.6667 | |||
| A= | 2 | 2 | 2 | B= | 1200 | |
| 1 | 2 | 4 | 1700 | |||
| Eliminating | ||||||
| 1 | 0.333333 | 1 | 466.6667 | |||
| A= | 0 | 1.333333 | 0 | B= | 266.6667 | |
| 0 | 1.666667 | 3 | 1233.333 | |||
| Normalizing the Matrix | ||||||
| 1 | 0.333333 | 1 | 466.6667 | |||
| A= | 0 | 1 | 0 | B= | 200 | |
| 0 | 1.666667 | 3 | 1233.333 | |||
| Eliminating | ||||||
| 1 | 0 | 1 | 400 | |||
| A= | 0 | 1 | 0 | B= | 200 | |
| 0 | 0 | 3 | 900 | |||
| Normalizing the Matrix | ||||||
| 1 | 0 | 1 | 400 | |||
| A= | 0 | 1 | 0 | B= | 200 | |
| 0 | 0 | 1 | 300 | |||
| Normalizing the Matrix | ||||||
| 1 | 0 | 0 | 100 | |||
| A= | 0 | 1 | 0 | B= | 200 | |
| 0 | 0 | 1 | 300 | |||
Thus, number of sheds that can be produced from the available hours of stamping, painting and packing are as following:
Shed 1 = 100 units
Shed 2 = 200 units
Shed 3 = 300 units
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