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

1. If the 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.
2. 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) The annual sales are as follows-

Market	Products
I	10,000	2,000	18,000
II	6,000	20,000	8,000

On writing in matrix form, `[(10000, 2000, 18000), (6000, 20000, 8000)]`

The selling price of each unit of products x, y, z is Rs 2.50, 1.50 and 1.00 respectively.

`[(2.50), (1.50), (1.00)]`

Income from both markets

`[(10000, 2000, 18000), (6000, 20000, 8000)] = [(2.50), (1.50), (1.00)]`

= `[(10000 xx 2.50 + 2000 xx 1.50 + 18000 xx 1.00), (6000 xx 2.50 + 20000 xx 1.50 + 8000 xx 1.00)]`

= `[(25000 + 3000 + 18000), (15000 + 30000 + 8000)] = [(46000), (53000)]`

Hence the income from each market is Rs. Rs 46,000 and Rs 53,000. Is.

(b) The cost price of each unit of each product x, y, z is Rs 2.00, 1.00 and 0.50 respectively.

On writing in matrix form,

`[(2.00), (1.00), (0.50)]`

The purchasing price in each market is as follows -

`[(10000, 2000, 18000), (6000, 20000, 8000)] = [(2.00), (1.00), (0.50)]`

= `[(10000 xx 2.00 + 2000 xx 1.00 + 18000 xx 0.50), (6000 xx 2.00 + 20000 xx 1.00 + 8000 xx 0.50)]`

= `[(20000 + 2000 + 9000), (12000 + 20000 + 4000)] = [(31000), (36000)]`

Total cost price = 31000 + 36000

= Rs. 67,000

Total selling price = 46000 = 53000

= Rs. 99,000

Profit = S.P - C.P = 99,000 - 67,000

= Rs. 32,000.