Find the level of production (in units) that will minimize the average cost. (Round your answer to the nearest whole number.)

Question

Minimizing Average Cost

 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

C(x) = 0.2(0.01x² + 114)

Answer 1

C(x) = 0.002x² + 22.8;

Average cost C(x) = C(x)/x = 0.002x + 22.8/x;

C'(x) = 0.002 - 22.8/x² = 0; 0.002x² = 22.8; x² = 11400; x = 107 units.

To prove that this production level gives minimum let find C''(x) = 45.6/x³ and C''(107) > 0