Question

A manufacturer produces three products $A,B,C$ which he sells in the market. Annual sale volumes are indicated as follows:

Markets	Product	Product	Product
	$A$	$B$	$C$
$I$	$8,000$	$10,000$	$15,000$
$II$	$10,000$	$2,000$	$20,000$

$\left(i\right)$ If unit sale prices of $A,B$ and $C$ are $Rs.2.25$, $Rs.1.50$ and $Rs.1.25$ respectively and If the unit costs of the above three products are $Rs.1.60$, $Rs.1.20$ and $Re.0.90$ respectively. Find the gross profit with the help of matrices
Ans in Rs. If it is 27kk0 Rs , find the value of k.

Answer 1

The total cost of product which the manufactures sells in the markets are given by the product matrix

$\left[\begin{array}{ccc}1.60& 1,20& 0.90\end{array}\right]\times \left[\begin{array}{cc}8,00& 10,000\\ 10,000& 2,000\\ 15,000& 20,000\end{array}\right]$

$=[(1.60\times 8,000)+(1.20\times 10,000)+(0.90\times 15,000)(1.60\times 10,000)+(1,20\times 2,000)+(0.90\times 20,000)]$

$=[12,800+12,000+13,500,16,500+2,400,18,000]$

$=[38,30036,400]$

Therefore the total cost of the product which the manufacture sell in the market is Rs 38,300 and Rs 36,400

Therefore required gross profit $=$( total revenue from the markets ) - (total cost os product which the manufacturer sold in both the market)

$=(51,150+50,500)-(38,300+36,400)$

$=102,250-74,700$

$=27,550$

$\therefore k=5$