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Question
The corner points of the feasible region of a linear programming problem are (0, 4), (8, 0) and `(20/3, 4/3)`. If Z = 30x + 24y is the objective function, then (maximum value of Z – minimum value of Z) is equal to ______.
Options
40
96
120
136
144
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Solution
The corner points of the feasible region of a linear programming problem are (0, 4), (8, 0) and `(20/3, 4/3)`. If Z = 30x + 24y is the objective function, then (maximum value of Z – minimum value of Z) is equal to 144.
Explanation:
| Corner Points | Z = 30x + 24y |
| (0, 4) | Z = 30 × 0 + 24 × 4 = 96 `rightarrow` Min. |
| (8, 0) | Z = 30 × 8 + 24 × 0 = 240 `rightarrow` Max. |
| `(20/3, 4/3)` |
Z = `30 xx 20/3 + 24 xx 4/3` = 200 + 32 = 232 |
Then Max. Z – Min. Z = 240 – 96 = 144.
Notes
The correct answer is not given as an option in the board paper
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