If a young man rides his motor cycle at `25 k . p . h`, he has to spend Rs. `2 per km` on petrol, if he rides it at ạ faster speed of `40k.p.h.`, the petrol cost increases to Rs. `5 per k m`. He has Rs. `100` to spend on petrol and wishes to find what is the maximum distance, he can travel within the hour. Express this as a linear programming problem and then solve it.

The price of petrol is 68.50 rupees per litre. What is the price of 8.5 litres?

A dealer manufactures ceiling fans and table fans. He has Rs. 9000 to invest and a store to keep atmost 75 pieces. A ceiling fan costs him Rs. 300 and a table fan Rs. 200. He expects a profit of Rs. 50 on a ceiling fan and Rs. 20 on a table fan. Assuming that he can sell all the fans that he manufactures, express it as a linear programming problem.

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for at most 20 items. A fan costs him Rs. 360 and a sewing a machine Rs. 240. His expectation is that he can sell a fan at a profit Rs. 22 and a sewing machine at a profit of Rs. 18 . Assuming that he can sell all the items that he can buy,how should he invest his money in order to maximise the profit? Formulate this as a linear programming problem and solve graphically.

A petrol tank is in the shape of a cylinder with hemisphere of the same radius as the base of the cylinder attached to both ends. How many litres of petrol can it hold?

A person inhales to his maximum capacity and then he exhales also to his maximum. What is the volume of air thus breathed out?

A furniture dealer deals only in two items - tables and 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 .Assume that he can sell all items that he buys. Using linear programming, formulate the problem for maximum profit.

In a business, total cost is Rs. 5000 . If the person gets Rs. 750 as profit, what is the percentage of profit he gets?.