Minimize $Z = 3x + 5y$ subject to $x + 3y \ge 3, x + y \ge 2, x \ge 0, y \ge 0$.
Step-by-Step Solution
Given: Minimize $Z = 3x + 5y$ subject to $x + 3y \ge 3, x + y \ge 2, x \ge 0, y \ge 0$.
Step 1: Set up the governing mathematical relation / formula:
From the given problem statement, we state the key relation:
$$Corner points (0,2):10, (3/2, 1/2):7, (3,0):9. Min Z$$
[1.0 Mark]
Step 2: Execute step-by-step evaluation and simplify:
Evaluating and simplifying the expression:
$$7 at (3/2, 1/2).$$
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Conclusion: The solution is verified as 7 at (3/2, 1/2)..
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🎯 Official CBSE Marking Scheme:
Setting up equation / formula: 1.0 Mark
Evaluating correct final answer: 1.0 Mark
Correct Answer: