The bookshop of a particular school has 10 dozen chemistry books , 8 dozen physics books, 10 dozen economics books . Their selling prices are Rs. 80, Rs, 60 and Rs.40 each respectively . Find the total amount the bookshop will receive from selling all the books using matrix algebra.

Three friends Ram , Shyam and Rahul went to a shop .Ram purchased 12 dozen notebooks ,6 dozen pen and 10 dozen pencil . Shyam purchased 20 dozen notebooks , 10 dozen pen and 15 dozen pencils . If the price of 1 dozen notebooks , pen and pencil is respectively Rs 72, Rs. 48 and Rs. 18 . Using matrix equation find the amount paid by each person to shopkeepar .

A manufacture produces three products x,y,z which he sells in two markets . Annual sales are indicated below : (a) If unit sale prices of x,yand 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 repectively .Find the gross profit.

In a development plan of a city, a contractor has taken a contract to construct certain houses for which he needs building materials like stones, sand etc. There are three firms A, B, C that can supply him these materials. At one time these firms A, B, C supplied him 40, 35 and 25 truck loads of stones and 10, 5 and 8 truck load of sand.If the cost of one truckload of stone and sand are Rs 1200 and 500 respectively, find the total amount paid by the contractor to each of these firms A, B, C separately.

(Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs. 10,500 and Rs. 9000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres per hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to to maximise the total profit of the society ?

(Allocation problem) A cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as rs. 10,500 and Rs. 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 litres and 10 litres pre hectare. Further, no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximise the total profit of the society?