A company decides to set up a production plant The total cost for initial set up is Rs - Maths - Linear Inequalities

Question

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

Shivam Mishra · Accepted Answer

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+300x⇒750x-300x>900000⇒450x>900000⇒x>900000450⇒x>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>100000⇒750x-900000+300x>100000⇒750x-300x-900000>100000⇒450x>900000+100000⇒450x>1000000⇒x>1000000450⇒x>2222
22But x cannot be fractional⇒x=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>150000⇒750x-900000+300x>150000⇒750x-300x-900000>150000⇒450x>900000+150000⇒450x>1050000⇒x>1050000450⇒x>2333
33But x cannot be fractional⇒x=2334Hence to realize profit gretaer than ₹150000,company shoud produce atleast 2334 units

Hope this information will clear your doubts about this topic

If you have any doubts just ask here on the ask and answer forum
and our experts will try to help you out as soon as possible
Regards