you're minimizing U(x) , not C(x).
U(x) = C(x)/x = 3000/x + 9 + 0.05x
U'(x) = -3000/x^2 + 0.05
U'(x) = 0 when x is approx 245.
In a certain manufacturing process, when the level of production is x units, the cost of production in dollars, is C(x)=3000+9x+0.05x^2, 1<=x<=300. What level of production x will minimize the unit cost U(x)=C(x)/x? Keep in mind that the production level must be an integer.
This is my work below.. it conflicts with the back of the book again. My answer is 34 and they have 245......
C'(x)=9+0.1x
c(1)=3009.05
c(300)=10200
3009.05/1=3009.05
10200/300=34
therefore the cost of production level should be 10200 dollars at 300 units or 34 dollars per unit.
so, is mine wrong and what did i do wrong?