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 ???

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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
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first, substitute n into the C equation to get: C=4000+12(600-10c)= 11200-120c then substitute n and C into P equation; P=c(600-12c)-(11200-120c) = -12(c^2)+720c-11200 differentiate P in term of c: dP/dc = -24c+720 note that the 2nd derivative is negative. therefore dP/dc is a max point. now let dP/dc=0, u will get c.

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