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For the given cost function C ( x ) = 19600 + 500 x + x 2 , First, find the average cost function. Use it to find: a) The production level that will minimize the average cost

Respuesta :

Answer:

The answer is "140".

Step-by-step explanation:

Calculating the average  cost:

[tex]= \frac{C(x)}{x}\\\\ = \frac{19600+500x+x^2}{x} \\\\ = \frac{19600}{x}+500 +x\\\\[/tex]

To minimize average cost we have to find x for wich A'(x)=0

[tex]A(x) = \frac{19600}{x}+500 +x \\\\A'(x) = -\frac{19600}{x^2}+1 \\\\0= -\frac{19600}{x^2}+1 \\\\\frac{19600}{x^2}=1 \\\\19600=x^2 \\\\x=140[/tex]