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Question

A manufacturer produces three products x,y,z which he sells in two markets. Annual sales are indicated below:
Market Products
I
10,0002,00018,000
II6,00020,0008,000
(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.

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Solution

(a) The unit sale prices of x,y and z are respectivelyRs.2.50,Rs.1.50 and Rs.1.00.

Total revenue in market I can be represented as:

[10000200018000]2.501.501.00
=10000×2.50+2000×1.50+18000×1.00
=25000+3000+18000
=46000

Total revenue in market II can be represented as:

[6000200008000]2.501.501.00
=6000×2.50+20000×1.50+8000×1.00
=15000+30000+8000
=53000

So, the total revenue in market I is Rs 46000 and in market II is Rs.53000.

(b) The unit cost prices of x,y and z are respectively given as Rs.2.00, Rs.1.00 and 50 paise.

So, the total cost prices of all the products in market I can be represented as:

[10000200018000]2.001.000.50
=10000×2.00+2000×1.00+18000×0.50
=20000+2000+9000
=31000

Since, the total revenue in market I is Rs.46000.
So, the gross profit in this market is Rs46000Rs31000=Rs15000.

The total cost prices of all the products in market II can be represented as:

[6000200008000]2.001.000.50
=6000×2.00+20000×1.00+8000×0.50
=12000+20000+4000
=Rs36000
Since, the total revenue in market II is Rs.53000.
So, the gross profit in this market is Rs.53000Rs.36000=Rs.17000.

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