Two godowns A and B have grains capacity of 100 quintals and 50 quintals respectively.They supply to 3 ration shop D,E,F whose requirement are 60,50 and 40 quintals respectively.The cost of transportation per quintal from the godowns to the shops is given in the following table,
transportation cost per quintal(in Rs).
Hence should the supplies be transported in order that the transportation cost is minimum?What is the minimum cost?

A farm is engaged in breeding pigs. The pigs are fed on various products grown on the farm. To ensure certain nutrient constituents X,Y and Z, It is necessary to mix two types of feeds A and B . One unit of product A contains 36 units of X, 3 units of Y and 20 units of Z. One unit of product B contains 6 units of X, 12 units of Y and 10 units of Z. The minimum requirement of X,Y and Z is 108 units, 36 units and 100 units respectively. Product A costs Rs. 20/unit and product B costs Rs 40/unit. Formulate this problem sa a linear programming problem to minimize the total cost.

A man owns a field of area 1,000 sq.m. He wants to plant fruit trees in it. He has a sum of Rs. 1,400 to purchase young trees. He has the choice of two types of the tree. Type A requires 10 sq.m of ground per tree and cost. Rs. 20 per tree and type B requires 20 sq.m of ground per tree and cost Rs. 25 per tree. When fully grown, type A produces an average of 20 kg fruit Which can be sold at a profit of Rs. 2 per kg and type B produces. an average of 40 kg of fruit which can be sold at a profit.of Rs. 1.50 per kg. How many of each type should he plant to achieve maximum profit when the trees are fully grown? What is the maximum profit?

Tailor Raju is available on daily wages rs 600 per day and Somu on rs 620 per day. Raju can stitch 6 shirts and 5 pants per day while Somu can stitch 10 shirts and 3 pants per day. In order to stitch 60 shirts and 40 pants in the minimum cost of production, how many days each Raju and Somu should work? What should be the minimum cost of production?