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?

A firm manufactures two types of products A and B and sells them at a profit of Rs. 5 per unit of type A and Rs. 3 per unit of type B . Each product is processed on two machines M_1 and M_2 . One unit of type A requires one minute of processing time, on, M_1 and two minutes of processing time on M_2 whereas one unit of type B requires one minute of processing time on M_1 and one minute of M_2 . Machines M_1 and M_2 are respectively available for at most 5 hours and 6 hours a day. Find how many, units of each type of product should the firm produce a day, in order, to maximise the profit. Solve thè problem graphically.

A manufacture company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing and B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hours available are 180 and 30 respectively per week. The company makes a profit of Rs. 8000/- on each piece of Model A and Rs. 12000/- on each piece of Model B. How many piece of Model A and B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

A manufacturer makes two types of tea cups, say A and B. Three machines are needed for the manufacturing and the time in minutes required for each cup on the machine is given below: Each machine is available for a maximum of 6 hrs per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. Show that 15 tea cups of type A and 30 tea cups of type B should be manufactured in a day to get the maximum profit.

A company produces two types of goods, A and B , that require gold and silver. Each unit of type A requires 3 gm of silver and 1 gm of gold while that of type B requires 1 gm of silver and 2 gm of gold. The company can use 9 gm of silver and 8 gm of gold. If each unit of type A brings a profit of Rs. 40 and that of type B Rs. 50 , find the number of units of each type that the company should produce to maximise the profit. What is the maximum profit.

A factory manufactures two types of screws, A and B . Each type of screw requires the 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 screw 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 eách type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

A manufacturer makes two types of tea cups, say A and B. Three machines are needed for the manufacturing and the time in minutes required for each cup on the machine is given below: Each machine is available for a maximum of 6 hrs per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. If x and y denote the number of cups of ttpe A and B produced in a day respectively. What is the profit function ?

The minute hand of a clock is 18 cms long. How many centimetres does the extremity of the minute hand move in 10 minutes?

A manufacture make two types of furniture,chairs and tables.Both the products are processed on three machines A_1,A_2 and A_3 .Machine A_1 requires 3 hours for a chair and 3 hours for a table,machine A_2 requires 5 hours for a chair and 2 hours for a table and machine A_3 requires 2hours for a chair and 6 hours for a table.Maximum time available on machine A_1,A_2 and A_3 is 36 hours,50 hours and 60 hours respectively.Profits are Rs.20 per chair and Rs.30 per table.Formulate the above as a linear programming problem to maximize the profit.