A company decides to set up a production plant . The total cost for initial set up is Rs. 900000 , the additional cost for producing each unit is Rs. 300 , each unit is sold at Rs. 750 . How many units must be produced and sold :
1) to realize a profit
2) to realize a profit of more than Rs. 100000
3) to realize a profit of more than Rs. 150000

Dear Student,
Please find below the solution to the asked query:

Initial cost= 900000Cost of production per piece=300Selling prive of each unit=750After production of x units,Total captial used =900000+300xFor realization of profit,750x>900000+300x750x-300x>900000450x>900000x>900000450x>2000Hence to realize profit,company shoud produce atleast 2001 units.Again,For profit gretaer than 100000Selling price of x units -Cost price of x units>100000750x-900000+300x>100000750x-300x-900000>100000450x>900000+100000450x>1000000x>1000000450x>2222.22But x cannot be fractionalx=2223Hence to realize profit gretaer than 100000,company shoud produce atleast 2223 units.Again,For profit gretaer than 150000Selling price of x units -Cost price of x units>150000750x-900000+300x>150000750x-300x-900000>150000450x>900000+150000450x>1050000x>1050000450x>2333.33But x cannot be fractionalx=2334Hence to realize profit gretaer than 150000,company shoud produce atleast 2334 units.

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