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.

Simple machines

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?

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.

Find the ratio of each of the in simplest form : 2 hours 45 minutes to 1 hour 15 minutes

A manufacturing company makes two models A and B of a product. Each piece of mode a requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Mode B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricati2 and finishing, the maximum labour hours available are 180 and 30 respectively. 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 pieces of Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

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 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.

(Manufacturing problem) A manufacturing 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. Each piece of Model 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. 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-pieces of Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

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.