(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

A furniture dealer deals in only two items - tables and chairs. He has Rs. 50,000 to invest and has storage pince of at most 60 pieces. A table costs Rs. 2500 and a chair Rs. 500. He estimates thnt from the sale of one table , he can make a profit of Rs. 250 and that from the sale of one chair a profit of Rs. 75. How many tables and chairs he should buy from the available money so as to maximise his total profit assuming that he can self all the items which he buys.

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: {:("Market",,"Products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (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.

In a legislative assembly election, a political group hired a public relations firm to promote its candidate in three ways: telephone, house calls, and letters. The cost per contact (in paise) is given in matrix A as A=overset("Cost per contact")([(,40,),(,100,),(,50,)]){:("Telephone"),("Housecall"),("Letter"):} The number of contacts of each type made in two cities X and Y is given by B=overset("Telephone Housecall Letter")(" "[(1000,500,5000),(3000,1000,"10,000")]){:(toX),(toY):} . Find the total amount spent by the group in the two cities X and Y.