SOLUTION: can you please help me whith this problem 64. Minimizing cost. A company uses the formula C(x) = 0.02x^2 � 3.4x + 150 to model the unit cost in dollars for producing x stabilizer

Question 60638: can you please help me whith this problem
64. Minimizing cost. A company uses the formula C(x) = 0.02x^2 � 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars id the unit cost at its minimum? What is the unit cost at level of production?

Answer by uma(370) (Show Source): You can put this solution on YOUR website!
C(x) = 0.02x^2 - 3.4x + 150
Differentiating the above with respect to x,
C '(x) = (0.02)(2)x - 3.4 + 0 [because differential of a constant is zero.]-(1)
Equating C '(x) to zero,
==> (0.02)(2)x - 3.4 = 0
==> 0.04x - 3.4 = 0
==> 0.04x = 3.4
==> 0.04x/0.04 = 3.4/0.04
==> x = 85
Now differentiating equation (1) again we get..
C '' (x) = 0.04 which is positive.
So x = 85 units the unit cost is minimum.

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