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Linear Programming
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
A furniture dealer deals in two items: tables and chairs. He has Rs 50,000 to invest and has storage space for at most 60 pieces. A table costs Rs 2500 and a chair costs Rs 500. He estimates that from sale of one table, he can make a profit of Rs 250 and that from a chair, a profit of Rs 75. How many tables and chairs should he buy to maximize profit?
Step-by-Step Solution
Given: A furniture dealer deals in two items: tables and chairs. He has Rs 50,000 to invest and has storage space for at most 60 pieces. A table costs Rs 2500 and a chair costs Rs 500. He estimates that from sale of one table, he can make a profit of Rs 250 and that from a chair, a profit of Rs 75. How many tables and chairs should he buy to maximize profit? Step 1: Formulate initial mathematical setup / substitution: Given equation / conditions: $$x + y <$$ [1.0 Mark] Step 2: Perform intermediate algebraic / calculus operations: Executing the step-by-step reduction: $$50000. Max Z$$ [1.0 Mark] Step 3: Evaluate final values / boundary conditions: Substituting limits or solving the simplified system: $$Rs 6250.$$ [1.0 Mark] Conclusion: The final evaluated answer is Rs 6250..
--- 🎯 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:
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