production levels

[SilentSymphony]

Using the formula c(x) = x^3 -20x^2 +20,000 (in which c(x) is the cost to produce x items), find a production level that will minimize the average cost of making x items.

 

[Deleted member 4993]

Please show us your work - what you have tried even if you think it is wrong and exactly where you are stuck.

 

[SilentSymphony]

okay, this one is the same as all of the other ones im having trouble with.

c(x) =x^3 -20x^2 +20000x

so now i need to differentiate and then set the derivative equal to zero to find my values:

c'(x) = 3x^2 -40x +20000
x (3x-40) + 20000 = 0
x (3x-40) = -20000

i just dont know how to get the value of x from there, or if i'm even doing it right...

 

[galactus]

Since you're in calc, you should know how to solve a quadratic.

Use the quadratic formula. That's always an old standby

 

[tkhunny]

c(x) =x^3 -20x^2 +20000x

1) If you cannot solve a quadratic equation, you will not survive calculus. What else re you missing from Algebra 1?

2) You do not seem to have the idea on this problem.

Cost to Produce x items.
c(x) = x^3 - 20x^2 + 20000

Average Cost of x items
a(x) = c(x)/x = x^2 - 20x + 20000/x

Find the minimum value

a'(x) = 2x - 20 - 20000/(x^2)

Find x, such that 2x - 20 - 20000/(x^2) = 0

As this results in a cubic equation, I suspect you will not have an easy time with this, either. In my mind, you had better go have a real serious chat with your teacher.

 

[Deleted member 4993]

SilentSymphony,

You gave us two different expressions for c(x)

Which one is correct?