producing widgets using a cost function----is this correct?

[kggirl]

C[x] = 10,000 + 50x-0.1x^3/2

1. What is the average cost per widget if you produce 10,000?

I don't know how to handle the exponent here (^3/2). I think this is how the problem goes:

10,000 + 50(10,000) - 0.1(10,000)^3/2 =
10,000 + 50,000 - 0.1(10^6)=
10,000 + 50,000 -1,000000 = 410,000

then you divide by 10,000 widgets ------ 410000/10,000 = 41.00 per widget

2. If you have produced 10,000 widgets, what is the marginal cost to make 1 more?

10,000 + 50x -0.1x^3/2 = (take the derivative of this)
0 + 50 - 0.1^6 = 49.99

Please let me know if this is correct

 

[tkhunny]

Re: producing widgets using a cost function----is this corre

C[x] = 10,000 + 50x-0.1x^3/2

You have not defined this. Is this the total cost function? You should say so.

1. What is the average cost per widget if you produce 10,000?

I don't know how to handle the exponent here (^3/2). I think this is how the problem goes:

10,000 + 50(10,000) - 0.1(10,000)^3/2 =

Good, so far.

10,000 + 50,000 - 0.1(10^6)=

The exponent looks good. The middle term doesn't. You have only 5*(10000).

10,000 + 50,000 -1,000000 = 410,000

0.1*10^6 = 10^5 It appears you missed that. How do you get 410000 after subtracting One Million from 60000? Shouldn't it be negative?

You simply must be more careful.

Try this:

c(x) = 10000 + 50*x - 0.1*x^(3/2)
c(x) = 10000 + 50*x - 0.1*x*x^(1/2) for x > 0

c(10000) = 10000 + 50*10000 - 0.1*10000*10000^(1/2)
c(10000) = 10000*(1 + 50 - 0.1*10000^(1/2))
c(10000) = 10000*(51 - 0.1*100)
c(10000) = 10000*(51 - 10)
c(10000) = 10000*(41)

c(10000)/10000 = 10000*41/10000 = 41

I think I understand how you managed 410000 from that subtraction. You had the answer already and ignored what you had written. Don't do that.