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A company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs ₹ 20 per kg and sand costs ₹ 6 per kg. Strength consideration dictate that a concrete brick should contain minimum 4 kg o…

Q.5 (A) (ii) A company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs ₹ 20 per kg and sand costs ₹ 6 per kg. Strength consideration dictate that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Formulate the L.P.P. for the cost to be minimum.

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Answer: Minimize \(z=20x+6y\) subject to \(x+y\ge5,\ x\ge4,\ y\le2,\ x\ge0,\ y\ge0\).

Let a brick contain x kg of cement and y kg of sand.

  • Cost: \(z=20x+6y\) (to be minimized).
  • Weight at least 5 kg: \(x+y\ge5\).
  • At least 4 kg cement: \(x\ge4\).
  • Not more than 2 kg sand: \(y\le2\).
  • Non-negativity: \(x,y\ge0\).
Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report
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