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Linear Programming
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Two tailors A and B earn Rs 150 and Rs 200 per day respectively. Tailor A can sew 6 shirts and 4 pairs of trousers per day, while B can sew 10 shirts and 4 pairs of trousers per day. How many days should each work to produce at least 60 shirts and 32 pairs of trousers at minimum labor cost?
Step-by-Step Solution
Given: Two tailors A and B earn Rs 150 and Rs 200 per day respectively. Tailor A can sew 6 shirts and 4 pairs of trousers per day, while B can sew 10 shirts and 4 pairs of trousers per day. How many days should each work to produce at least 60 shirts and 32 pairs of trousers at minimum labor cost? Step 1: Formulate initial mathematical setup / substitution: Given equation / conditions: $$6x + 10y >$$ [1.0 Mark] Step 2: Perform intermediate algebraic / calculus operations: Executing the step-by-step reduction: $$32. Min Z$$ [1.0 Mark] Step 3: Evaluate final values / boundary conditions: Substituting limits or solving the simplified system: $$Rs 1350.$$ [1.0 Mark] Conclusion: The final evaluated answer is Rs 1350..
--- 🎯 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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