Answer to Question #257224 in Linear Algebra for Ahmad

Question

a company in the wholesale trade selling sportswear and stocks two brands, a and b, of football kit, each consisting of a shirt, a pair of shorts and a pair of socks. the costs for brand a are sh.50 for a shirt, sh 30 for a pair of shorts and sh10 for a pair of socks and those for brand b are sh.60.25 for a shirt, sh.40 for a pair of shorts and sh.10 for a pair of socks. three customers x, y, z demand the following combinations of brands; x, 36 kits of brand a and 48 kits of brand b y, 24 kits of brand a and 72 kits of brand b z, 60 kits of branda required:i) express the costs of brands a and b in matrix form, then the demands of the customers, x,y and z in matrix form. (5 marks)ii) by forming the product of the two matrices that you obtain in the previous part, deduce the detailed costs to each of the customers. (5 marks)

Answer 1

i)

The costs of brands a and b:

shirt shorts socks

brand a 50 30 10

brand b 60.25 40 10

The demands of the customers:

$\begin{matrix} & \textrm{Brand \ A} & \textrm{Brand \ B} \\ \textrm{Customer \ X} & 36 & 48 \\ \textrm{Customer \ Y} & 24 & 72 \\ \textrm{Customer \ Z} & 60 & 0 \\ \end{matrix}$

ii)

detailed costs to each of the customers:

$\begin{pmatrix} 36 & 48 \\ 24 & 72\\ 60&0 \end{pmatrix}\begin{pmatrix} 50 & 30&10 \\ 60.25 & 40&10 \end{pmatrix}=\begin{pmatrix} 4692 & 3000& 840 \\ 5538 & 3600& 960 \\ 3000 & 1800&600 \end{pmatrix}$

$\begin{matrix} & \textrm{ shirt} & \textrm{shorts}& \textrm{socks} \\ \textrm{Customer \ X} & 4692 & 3000&840 \\ \textrm{Customer \ Y} & 5538 & 3600&960 \\ \textrm{Customer \ Z} & 3000 & 1800&600 \\ \end{matrix}$