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?

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 factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

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.

Cost of an item is Rs.50. It was sold with a profit of 12%. Find the selling price.

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 whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each 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 sell all the items that she produced? What will be the maximum Profit?