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Class 12 Matrices · Case Study4 Marksmatrix_applications

Class 12 Maths · Matrices · Case Study #30

A manufacturer sells pencils, erasers and sharpeners in two markets. Annual quantities are in the attached data table. Unit selling prices are ₹2.50, ₹1.50 and ₹1.00 respectively; unit costs are ₹2.00, ₹1.00 and ₹0.50. Use matrix multiplication to compute the requested totals.
An illustrative view of two neighbourhood stationery shops selling pencils, erasers and sharpeners.
An illustrative view of two neighbourhood stationery shops selling pencils, erasers and sharpeners.
Part (1) 1 Marks
Find the total revenue in market A.
Answer: ₹46,000
  1. Multiply the quantity row [10000,2000,18000] by the selling-price column [2.50,1.50,1.00]ᵀ: 25000+3000+18000.
  2. The total revenue in market A is ₹46,000.
Part (2) 1 Marks
Find the total revenue in market B.
Answer: ₹53,000
  1. The matrix row product is [6000,20000,8000][2.50,1.50,1.00]ᵀ=15000+30000+8000.
  2. The total revenue in market B is ₹53,000.
Part (3) 1 Marks
Alternatively, find the cost incurred in market A.
Answer: ₹31,000
  1. Multiply the market A quantity row by the unit-cost column: 10000·2+2000·1+18000·0.50=20000+2000+9000.
  2. The total cost in market A is ₹31,000.
Part (4) 2 Marks
Find the profit in each market.
Answer: Market A: ₹15,000; market B: ₹17,000.
  1. The per-unit profit column is price minus cost: [0.50,0.50,0.50]ᵀ.
  2. Multiply the two quantity rows by that column: A gives 5000+1000+9000=15000; B gives 3000+10000+4000=17000. Equivalently revenues ₹46000,₹53000 minus costs ₹31000,₹36000 give the same results.
  3. Thus the profits are ₹15,000 in A and ₹17,000 in B.

✅ Step-by-Step Solution

Review the worked subparts and marking breakdown above.

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