In a small scale industry, a manufacturer produces two types of book cases. The first type of book case requires 3 hours on machine A and 2 hours on machine B for completion whereas the second type of book case requires 3 hours on machine A and 3 hours on machine B. The machines A and B respectively run for at the most 18 hours and 14 hours per day. He earns a profit of 30 on each type of case of first type and 40 on each book case of second type. How many book cases of each type should he manufacture so as to have maximum profit. Make it an LPP and solve it graphically.

A manufacture produceds two types of steel trunks. He has two machines, A and B. The first type of book case requires 3 hours on machine A and 3 hours on machine B for completion whereas the second type required 3 hours on machine A and 2 hours n 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 second type respectively. How many trunks of each type must he make each day to make the maximum 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?

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 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 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 manufacturer produces two types of soaps using two machines A and B . A is operated for 2 minutes and B for 3 minutes to manufacture first type , while it takes 3 minutes on machine A and 5 minutes on machine B to manufature second type . Each machine can be operated at the most for 8 hours per day . The two types of soap are sold at a profit of Rs 0.25 and Rs 0.05 each respectively . Assuming that the manufactured can sell all the soaps he can manufacture , how many soaps of each type should be manufature per day so as to maximize his profit .

A furniture firm 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 machine A and B and 3 hours on machine C. The profit obtained by selling on chair is ₹ 30 while by selling one table the profit is ₹ 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 tables should be made per week so as to maximize profit ? Formulate the problem as L.P.P. and sovle it graphically.

A manufaturer makes two types of toys, A and B cups. Three machines are needed for the the manufacture and the time in minutes required for each cup on the machines in given below: Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.5 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get the maximum profit.

A manufacturer makes two type of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below : Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs. 7.50 and that on each toy of type B is Rs. 5, whow that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.