The cost of producing commodity is C(X)=3X^2+4X+8 dollars.If the price is P(X)=(50-X) dollars per unit,determine the level of production that maximizes the profit.

Question

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What is the level of production.

Answer 1

profit=(price-cost)x
= 50x-x^2 -3x^3-4x^2-8x

dprofit/dx=0= 50-2x-9x^2-8x-8

9x^2-10x+42=0

x= (10+sqrt(10000-1512))/18 =5.6
since you cant produce .6 of the units, try x=6, and x=5 to see which is the greater profit.

check my thinking and work.