anonymous
  • anonymous
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 ???
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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.

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