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Linear Programming
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
A merchant plans to sell two types of personal computers — desktop model and portable model that will cost Rs 25,000 and Rs 40,000 respectively. He estimates total yield of computers will not exceed 250 units. Total investment capacity is Rs 70 lakhs. Profit on desktop is Rs 4500 and on portable is Rs 5000. Determine number of units of each type to maximize profit.
Step-by-Step Solution
Given: A merchant plans to sell two types of personal computers — desktop model and portable model that will cost Rs 25,000 and Rs 40,000 respectively. He estimates total yield of computers will not exceed 250 units. Total investment capacity is Rs 70 lakhs. Profit on desktop is Rs 4500 and on portable is Rs 5000. Determine number of units of each type 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: $$7000000. Max Profit Z$$ [1.0 Mark] Step 3: Evaluate final values / boundary conditions: Substituting limits or solving the simplified system: $$Rs 11,50,000.$$ [1.0 Mark] Conclusion: The final evaluated answer is Rs 11,50,000..
--- 🎯 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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