Question

A manufacturer produces three products x , y , z which he sells in two markets. Annual sales are indicated below: Market Products I 10000 2000 18000 II 6000 20000 8000 (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. (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.

Answer 1

(a)

Let, the sales of products x, y and z per market be denoted by matrix A that is,

A=[ 10000 2000 18000 6000 20000 8000 ]

Let, the unit sale price of products x, y and zper market be denoted by matrix B that is,

B=[ 2.50 1.50 1.00 ]

Now, the total revenue is equal to the product of total sales and unit sales price.

Total Revenue=AB =[ 10000 2000 18000 6000 20000 8000 ][ 2.50 1.50 1.00 ] =[ 10000( 2.50 )+2000( 1.50 )+18000( 1.00 ) 6000( 2.50 )+20000( 1.50 )+8000( 1.00 ) ] =[ 46000 53000 ]

Thus, the total revenue of the market I is 46000 rupees, and the total revenue of the market II is 53000rupees.

(b)

For the gross profit, consider the unit cost price of the products x, y and z per market be denoted by matrix C that is,

C=[ 2.00 1.00 0.50 ]

Now, the total cost of the commodities (T.C.) is equal to the product of total sales and unit cost price.

T.C.=AC =[ 10000 2000 18000 6000 20000 8000 ][ 2.00 1.00 0.50 ] =[ 10000( 2.00 )+2000( 1.00 )+18000( 0.50 ) 6000( 2.00 )+20000( 1.00 )+8000( 0.50 ) ] =[ 31000 36000 ]

Now, the gross profit (G.P.) is equal to the difference of revenue and cost.

G.P.=[ 46000 53000 ]−[ 31000 36000 ] =[ 15000 17000 ]

Thus, the total profit of the market I is

15000 rupees and the total profit of the market II is 17000 rupees.