Misc 10 - A manufacturer produces three products x, y, z - Miscellaneous

  1. Chapter 3 Class 12 Matrices
  2. Serial order wise
Ask Download

Transcript

Misc. 10 A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000 II 6,000 20,000 8,000 (a) If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively. Find the total revenue in each market with the help of matrix algebra. Let the sales of products x , y & z per market be denoted by matrix A A = [■8(10,000&2000&18,000@6,000&20,000&8,000)] Let the unit sale price of products x , y & z per market be denoted by matrix B Let B = [■8( 2.50 @1.50@1.00)] Now, Total Revenue = Total sales × Unit sales price = AB = [■8(10,000&2000&18,000@6,000&20,000&8,000)]_(2×3) [■8(2.50@1.50@1.00)]" " _(3×1) = [■8(10,000(2.50)+2000(1.50)+18,000(1)@6,000(2.50)+20,000(1.50)+8,000(1) )] = [■8(25,000+3,000+18,000@15,000+30,000+8,000)] = [■8(46,000@53,000)] Total Revenue = [■8(46,000@53,000)] Hence, Total revenue of Market I = Rs. 46,000 & Total revenue of Market II = Rs. 53,000 Misc. 10 A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000 II 6,000 20,000 8,000 (b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit. Let the unit cost price of products x , y & z per market be denoted by matrix C Let C = [■8( 2.00 @1.00@0.50)] Now, Total Cost = Total sales × Unit cost price = AC = [■8(10,000&2000&18,000@6,000&20,000&8,000)]_(2×3) [■8(2.00@1.00@0.50)]" " _(3×1) = [■8(10,000(2.00)+2000(1.00)+18,000(0.50)@6,000(2.00)+20,000(1.00)+8,000(0.50) )] = [■8(20,000+2,000+9,000@12,000+20,000+4,000)] = [■8(31,000@36,000)] Now, Profit = Revenue – Cost = [■8(46,000@53,000)] – [■8(31,000@36,000)] = [■8(15,000@17,000)] Thus, Profit = = [■8(15,000@17,000)] Hence, Total profit of Market I = Rs. 15,000 & Total profit of Market II = Rs. 17,000

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.