A factory owner wants to purchase two types of machines A and B, for his factory. The machine A requries an area of `1000m^2` and 12 skilled men for running it and its daily output is 50 units. Whereas the machine B are requries `1200m^2` area and 8 skilled man, and its daily output is 40 units. if an area of `7600m^2` and 72 skilled men be availabe to operate the machines,how many machines of each type should be brought to maximize the daily output.

A factory owner purchases two types of machines A and B for his factory. The requirements and limtations for the machines are as follows: He has an area of 9000 sq m available and 72 skilled men who can operate the machines. How many machines of each type should he buy to maximize th daily output?

A factory owner purchases two types of machines, A and B fo his factory. The requirements and the limitation for the machines are as followes : He has maximum area of 9000 m^2 available, and 72 skilled labourers who can operate both the machines. How many machines of each type should be buy to maximise the daily output ?

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?

A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

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 furniture firm manufactues chairs and tables, each requairing the use of three machines A,B and C. Producing of 1 chair requires 2 hours of machine A, 1hour 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 realised by selling 1 chair is Rs 30 while for a table 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. Find the mathematical formulation so as to find the number of chairs and tables that should be made per week soto maximizethe profit.