Mohan is a carpenter who specialises in making chairs. For every assignment he undertakes, he charges his commission and cost. His commission is fixed and equals Rs.560 per assignment while the cost equals Rs.2n² where n is the total number of chairs he makes. If for a certain assignment the average cost per chair is not more than Rs.68 then the minimum and maximum possible number of chairs in the assignment are, respectively.

Option
(1) 13 and 19
(2) 13 and 20
(3) 14 and 19
(4) 14 and 20

• Option 4: 14 and 20
  
  Given Carpenter's commission is fixed = Rs.560
  also given cost of making chairs is 2n^2 ( n is number of chairs)
  
  Given for certain assignment the average cost per chair is not more than Rs.68
  that is
  
  560+(2n^2)/n=68
  (560 is fixed commission and "n" is number of chairs and "2n^2" is cost of making chairs)
  =>
  560+(2n^2)=68n
  =>(2n^2)-68n+560=0
  dividing the above equation by 2(in order to simplify it)
  therefore (n^2)-34n+280=0
  =>(n^2)-20n-14n+280=0 (by factorization)
  =>n(n-20)-14(n-20)=0
  =>(n-20)(n-14)=0
  therefore "n" has 20 and 14
  so the maximum number of chairs in the assignment are 20 and
  minimum number of chains in the assignment are 14
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