A particular factory manufactures (n) units per month.Each unit sells for (c) dollars.The number of units sold varies with the selling price according to ;
n=600-10c
and the monthly operating cost of the factory is given by;
C=$4000+12n
The monthly profit;
P=nc-C is a maximum when the unit selling price is ???

Question

A particular factory manufactures (n) units per month.Each unit sells for (c) dollars.The number of units sold varies with the selling price according to ;
   n=600-10c
and the monthly operating cost of the factory is given by;
  C=$4000+12n
The monthly profit;
   P=nc-C  is a maximum when the unit selling price is ???

anonymous · Answer

You have n and C given to you in terms of c, and you're looking for that particular c that will maximize the function, P.  I don't know what level calculus you're doing, but you can do this a couple of ways.

Since you need to maximize P(c), one thing you can do is sub. each expression for n and C into P in terms of c and take the derivative.  So,$$P=(600-10c)c-(4000+12(600-10c))$$ $$=3800+120c-100c^2$$
Then $$P'(c)=120-200c \rightarrow c=\frac{120}{200}=\frac{3}{5}=$0.60$$Please check everything, I'm half asleep.