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Class 12 Matrices · Long Answer3 Marksmatrix_applications

Class 12 Maths · Matrices · Long Answer #104

A manufacturer sells products x,y,z in markets I,II. The attached table gives annual quantities. Unit selling prices are ₹2.50,₹1.50,₹1.00 respectively. Find each market’s total revenue using matrices.

✅ Step-by-Step Solution

Final Answer: Market I: ₹46,000; market II: ₹53,000.
  1. Use quantity matrix Q=[[10000,2000,18000],[6000,20000,8000]] and selling-price column p=[2.50,1.50,1.00]ᵀ.
  2. The first row product is 10000·2.50+2000·1.50+18000·1.00=25000+3000+18000=46000.
  3. The second row product is 6000·2.50+20000·1.50+8000·1.00=15000+30000+8000=53000.
  4. Thus Qp=[46000,53000]ᵀ: revenues are ₹46,000 in I and ₹53,000 in II.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use quantity matrix Q=[[10000,2000,18000],[6000,20000,8000]] and selling-price column p=[2.50,1.50,1.00]ᵀ.
  • [1 mark] The first row product is 10000·2.50+2000·1.50+18000·1.00=25000+3000+18000=46000.
  • [1 mark] The second row product is 6000·2.50+20000·1.50+8000·1.00=15000+30000+8000=53000.
  • [0.5 marks] Thus Qp=[46000,53000]ᵀ: revenues are ₹46,000 in I and ₹53,000 in II.

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