Rita N.

asked • 06/26/17

Business Calculus minimum average cost per unit

Hello, I have a problem I just can't figure out. It calls for me to find the minimum cost per unit and the maximum cost per unit of c(x)= 0.003x^3 + 7x + 9858     Please explain the steps. Thank you for any help with this problem.

Sava D.

tutor
Check your cost function. The way it is written, there is no minimum cost. It is common sense. When x increases, x3 increases +7x increases and +9885 stays the same. I assume x>=0, because it is cost function.
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06/26/17

Rita N.

Sava, That is not what my calculus homework says; "Suppose that the cost function for a product is given by C+ 0.003x cubed + 6x + 11,719. Find the production level (i.e., value of x) that will produce the minimum average cost per unit." Sorry, I am sleep deprived and left out the word average. X has to be greater than zero. I get to the part where I am to divide and cannot get the correct answer.
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06/27/17

1 Expert Answer

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Kenneth S. answered • 06/26/17

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Cost PER UNIT = c(x)/x = 0.003x+ 7 + 9858/x = f(x) and so f'(x) = 0.006x + 9858(-1)(x-2),
 
setting f' to zero yields 0.006x = 9858/x2 and that yields x = 118.
 
So that's the critical point.  You can complete the discussion...
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Rita N.

I see what you have written. Perhaps it is lack of sleep (I'm taking a semester of calculus in a 4 week summer class) But I cannot for the life of me get 118 when I divide as the online book says to do. 9858/0.006x is not 118. I know I am missing a step somewhere, but all that the explanation says in an example given is to divide. That is the explanation I was looking for. Thank you.
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06/27/17

Kenneth S.

f' = 0 ⇔ 0.006x = 9858/x2  ...  do you agree?
 
Multiplying by x squared on each side gives 0.006x3 = 9858
so do two things:
1) divide each side by 0.006 to isolate x cubed
2) then take CUBE ROOT of the quotient developed in step 1 above.  
 
DO YOU AGREE NOW?
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06/27/17

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