Question

A salesperson Ravi has the following record of sales for the month of January, February, and March 2009 for three products A, B, and C. He has been paid a commission at a fixed rate per unit but at varying rates for products A, B and C.

Months	Sales in Units			Commission
	A	B	C
January	9	10	2	800
February	15	5	4	900
March	6	10	3	850

Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.

Answer 1

Let x, y and z be the rate of commission for the three products A, B and C respectively. 

9x + 10y + 2z = 800

15x + 5y + 4z = 900 

6x + 10y + 3z = 850 

The given system can be written as

= 9[15 – 40] – 10(45 – 24) + 2(150 – 30) 

= 9[-25] – 10[21] + 2[120] 

= -225 – 210 + 240 

= -195

X = A^-1B 

∴ x = 17.95, y = 43.08, z = 103.85

The rate of commission of A, B and C are 17.95, 43.08 and 103.85 respectively.