Respuesta :
Answer:
C(x) = 53 $
Step-by-step explanation: Incomplete question. From google the question is (paste)
Suppose the total cost function for manufacturing a certain product C(x) is given by the function below, where C (x) is measured in dollars and x represents the number of units produced. Find the level of production that will minimize the average cost. (Round your answer to the nearest whole number.)
C(x)=0.2(0.01x^2+133)
If C(x) = 0.2(0.01x^2+133) ; and x numbers of produced units, the average cost is
Ca(x) = ( 0,002*x² + 26,6) /x ⇒ Ca(x) = 0.002*x + 26.6/x
Taking derivatives on both sides of the equation
Ca´(x) = 0.002 - 26.6/x² Ca´(x) = 0
0.002 - 26.6/x² = 0 ⇒ 0.002x² -26.6 = 0
x² = 26.6 /0.002
x = 115,33 ⇒ x = 115 units
And the level of production will be
C(x)=0.2(0.01x^2+133)
C(x)= 0.002*x² + 26,6
C(x)= 26.45 + 26,60
C(x)= 53.05 $
C(x) = 53 $
