Manufacturer produces two types of steel trunks. He has two machines, A and B. The first type of trunk requires 3 hours on machine A and 3 hours on machine B. The second type requires 3 hours on machine A and 2 hours on machine B. Machines A and B can work at most for 18 hours and 15 hours per day respectively. He earns a profit of Rs. 30 per trunk on the first type of trunk and Rs. 25 per trunk on the second type. Formulate a linear programming problem to find out how many trunks of each type he must make each day to maximize his profit.

A manufacturer produces two types of steel trunks. He has tow machines A and B. For completing, the first types of the trunk requires 3 hours on machine A and 3 hours on machine B, whereas the second type of the trunk requires 3 hours on machine A and 2 hours on machine B. Machines A and B can work at most for 18 hours and 15 hours per day respectively. He earns a profit of Rs. 30 and Rs. 25 per trunk of the first type and the second respectively. How many trunks of each type must he make each day to makes maximum profit?

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machine for at most 12 hours a day?

A furniture form manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires 2 hours on machine A, 1 hour on machine B, and 1 hour on machine C. Each table requires 1 hour each on machines A and B and 3 hours on machine C. Profit realized by selling one chair is Rs. 30 while for a table the figure is Rs. 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours, and on machine C is 90 hours. How many chairs and table should be made per week so as to maximize profit? Develop a mathematical formulation.

A machine does 392 J of work in 4 seconds. What is the power of the machine?

A manufacturer produces nuts and bolts. It takes 2 hours work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 2 hours on machine B to produce a package of bolts. He earns a profit of Rs. 24 per package on nuts and Rs. 18 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 10 hours a day. Make an L.P.P. from above and solve it graphically ?

A company manufactures two types of screws A and B. all the screws have to pass through a threading machine and a slotting machine. A box of type A screw requires 2min on the threading machine and 3 min on the slotting machine. A box of type B screw requires 8 min on the threading machine and 2 min on the slotting machine. In a week each machine is availbale for 60h. On selling these screws, the company gets a profit of 100 box on type A screw and 170 per box on type B screws. Formulate this problem as a LPP given that the objective is to maximise profit.

A manufacturing companu makes two types of teaching aids A and B of Mathematics for Class X. Each type of A requires 9 labour hours for fabircating and 1 labour for finishing. Each type of B requires 12 labour hours for fabircating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of 80 on each piece of type A and 120 on each piece of type B. How many pieces of type A and types B should be manufactured per week to get a maximum profit? Formulae this as Linear Programming Problems and solved it. Identify the feasible region from the rough sketch.

Two taps A and B can fill an overhead tank in 10 hours and 15 hours respectively. Both the taps are opened for 4 hour and then B is turned off. How much time will A take to fill the remaining tank ?

A firm manufactures two products A and B. Each product is processed on two machines M_1a n dM_2 . Product A requires 4 minutes of processing time on M_1 and 8 min. on M_2 ; product B requires 4 minutes on M_1 and 4 min. on M_2 . The machine M_1 is available for not more than 8 hrs 20 min. while machine M_2 is available for 10 hrs. during any working day. The products A and B are sold at a profit of Rs. 3 and Rs. 4 respectively. Formulate the problem as a linear programming problem and find how many products of each type should be produced by the firm each day in order to get maximum profit.

A firm manufactures two types of products, A and B, and sells them at a profil of 3 per unit to type B product and 5 perunit of type A product. Both product is processed on two machines M1and M2 One unit of type A requires one minute of processing time on M1 and two minutes of processing time on M2i whereas one unit of type B requires one minute of processing time on M1 and one minute on M Machines sells them at a profit of 5 per unit of type A and M, and M, are respectively available for at most 5 hours and 6 hours in a day. Find out how many units of each type of product the firn should produce a day in order to maximize the profit. Solve the problem graphically [CHSE 2000]