for the given cost function C(x) = 54 sqroot x + x^2/27000

(a) find the production level that will minimize the avg cost
(b) find the minimal avg cost

This post was edited by xSuki on Dec 9 2013 11:27pm

isn't this just a parabola? find the point where it's lowest.

Part 1: find the derivative and set it equal to zero. If you get multiple values, use the first derivative test to determine if it's a minimum or maximum.
Part 2: then to find the minimal avg cost, plug in the value you find in Part 1 back into the original Cost function.

i just need the answers quick

i gave you the answer
(other thread)

This post was edited by JDota72 on Dec 9 2013 11:44pm

part 1 is 3214.49=x

part 2 other thread

This post was edited by JDota72 on Dec 9 2013 11:45pm

C(x) = 54*x^(1/2) + (x^2)/27000

To find the average cost function, you need to divide the total cost by the output (x)

Cavg(x) = 54*x^(-1/2) + x/27000

Now, to find the minimum, we will set the derivative of the function to zero and solve for x.

d/dx [54*x^(-1/2) + x/27000] = 0
-27x^(-3/2) + 1/27000 = 0 ...take derivative
-27x^(-3/2) = -1/27000 ...move constant to other side
x^(-3/2) = 1/729000 ...divide by sides by -27
x = (1/729000)^(-2/3) ...^-2/3 on each side
x = 8100


To find the minimum average cost, just plug our value of x back into our Cavg function

Cavg(x) = 54*x^(-1/2) + x/27000
Cavg(8100) = 54*8100^(-1/2) + 8100/27000
Cavg(8100) = 0.9