(Allocation Problem.)A farmer has 5 acres of land on which he wishes to grow two crops X and Y. He has to use 4 cart loads and 2cart loads of manure per acre for crops X and Y respectively. But not more than 18 cart loads of manure is available. Other expenses are ₹200 and ₹500 per acre for the crops X and Y respectively . He estimates profit from crops X and Y at the rates ₹1000 and ₹800 per acre respectively. Formulate the LPP as to how much land he should allocate to each crop for maximum profit.

Let X and Y be sets containing m and n elements respectively.What is the total number of functions from X to Y.

A merchant sells two models X and Y of TV with cost price ₹ 25000 and ₹ 50000 Per set respectively. He gets a profit of ₹ 1500 on model X and ₹ 2000 on model Y . The sales connot exceed 20 sets in a month. If he cannot invest more than 6 lakh rupees, formulate the problem of determining the number of sets of each type he must keep in stock for maximum profit.

A company has two factories at locations X and Y. He has to deliver the products from these factories to depots located at A, B and C. The production capacities at X and Y are respectively 12 and 10 units and the resquirements at the depote are 8,8 and 6 units respectively. The cost of transportation from the factories to the depote per unit of the product given below. The company has to determine how many units of product should be transported from each factory to each depot so that cost of transportation is minimum. Formulate this problem as L. P. P.

If X and Y are sets containing m and n elements respectively then what is the total number of function from X to Y ?

The calcium salt used as manure is:

Write note on Bt-Crops.

A genetically modified crop is: