Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs 50 per metre and trouser material that costs him Rs 90 per metre. For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is Rs 36,600. How much trouser material did he buy?

A shopkeeper deals in two items: thermoflasks and airtight containers. A flask costs him Rs.120 and an airtight container costs him Rs.60. he has atmost Rs.12000 to invest and has space to store a maximum of 150 items. The profit on selling a flask is Rs.20 and that on airtiht container is Rs.15. assumint that he will be the able to sell all things to buys, how many of each item should be buy to maximise his profit? solve the problem graphically.

A fruit vendor buys some oranges at the rate of Rs 5 per orange. He also buys an equal number of bananans at the rate of Rs 2 per banana. He makes a 20% profit on orange and a 15% profit on bananas. At the end of the day, all the fruit is sold out. His total profit is Rs 390. Find the number of oranges purchased.

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 respectively. If the cost of one truckload of stone and sand are Rs 1200 and 500 respectively, then find the total amount paid by the contractor to each of these firms A, B, C separately.

A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs 5670 to invest and has a space for at most 20 items. An electronic sewing machine costs him Rs 360 and manually operated sewing machine Rs 240. He can sell electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assumning that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit. Make it a linear programming problem and solve it graphically. Keeping the rural background in mind justify the values to be promoted for the selection of the manually operated machine.

A furniture dealer deals in only two items tables chairs. He has Rs 5000 to invest and a space to store at most 60 pieces. A table costs him Rs 250 and a chair Rs 50. He can sell a table at a profit of Rs 50 and a chair at a profit of Rs 15. Assuming that he can sell all the items that he buys, how should he invest his money in order that he may maximize his profit?