For 6 cups of rice, 2 cups of urad should be taken to make dosas. How many cups of urad should taken with 9 cups of rice?

For a group photograph, 3 boys and 2 girls stand in a line in all possible ways. How many photos could be taken if each photo corresponds to each such arrangement

Fill in the blanks to make each of the following a true statement: A cup A'=

A company manufactures two types of rovelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs 5 each for type A and Rs 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?

Acid and water mixed in the ratio 3: 2 to make a 100 litre mixture. How many litres of acid should be added to change theratio to 3: 1 ?

A firm deals with two kinds of fruit juices-pineapple and the, orange juice. These are mixed and two types of mixtures are obtained which is sold as soft drinks A and B , One tin of A need 4 litres of pineapple juice and 1 litre of orange juice. One tin of B needs 2 litres of pineapple and 3 litres of oranges juice. The firm has only 46 litres of pineapple juice and 24 litres of orange jụice. Each tin of A and B is sold at a profit of Rs. 4 /- and Rs. 3 /-respectively. How many tins of A and B should the firm produce to maximise profiț? Formulate the linear programming problem and solve it graphically.

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?

(Manufacturing problem) A manufacturer has three machines I , II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours where as machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are given in the following table: She makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can swll all the items that she produced ? What will be the maximum profit ?