Solve LPP: Maximize $Z = 3x + 2y$ subject to $x + 2y \le 10, 3x + y \le 15, x, y \ge 0$.
Step-by-Step Solution
Given: Solve LPP: Maximize $Z = 3x + 2y$ subject to $x + 2y \le 10, 3x + y \le 15, x, y \ge 0$.
Step 1: Formulate initial mathematical setup / substitution:
Given equation / conditions:
$$Corner points (0,0):0, (5,0):15, (4,3):18, (0,5):10. Max Z$$
[1.0 Mark]
Step 2: Perform intermediate algebraic / calculus operations:
Executing the step-by-step reduction:
$$18 at (4, 3).$$
[1.0 Mark]
Step 3: Evaluate final values / boundary conditions:
Substituting limits or solving the simplified system:
$$18 at (4, 3).$$
[1.0 Mark]
Conclusion: The final evaluated answer is 18 at (4, 3)..
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🎯 Official CBSE Marking Scheme:
Formulating mathematical relation: 1.0 Mark
Executing algebraic/calculus operations: 1.0 Mark
Evaluating final solution/vector: 1.0 Mark
Correct Answer: