Question:
The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:
The maximum value of Z= 2x + 3y subject to the constraints x≥0, y>0; x+y≤ 10, 3x+4y≤ 36 is:
Updated On: Mar 27, 2026
- 20
- 27
- 30
- 0
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The Correct Option is B
Solution and Explanation
To determine the maximum value of Z=2x+3y given the constraints x≥0, y>0; x+y≤10, and 3x+4y≤36, we will use the graphical method for solving linear programming problems.
| Step | Description |
|---|---|
| 1 | Identify the feasible region by graphing the constraints on the xy-plane. |
| 2 | Graph x+y=10. This is a line passing through the points (0,10) and (10,0). |
| 3 | Graph 3x+4y=36. This line passes through (0,9) and (12,0). |
| 4 | Identify the feasible region where all constraints overlap, considering x≥0 and y>0. |
| 5 | Determine the vertices of the feasible region. They are (0,0), (0,9), (4,6), and (10,0). |
| 6 | Calculate Z=2x+3y for each vertex:
|
| 7 | Identify the maximum value: Z=27 at (0,9). |
The maximum value of Z is 27, confirming the correct answer is 27.
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