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January 30th, 2014, 12:08 PM   #1
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Marginal cost with two variables, confused.

Your weekly cost to manufacture x bicycles and y tricycles is

C(x,y)=20,000+60x+20y+50?(xy)

a. What is marginal cost of manufacturing a bicycle.
I derived x and got (25y^1/2)/x^(1/2) +60 but I dont know what to do next or if that is even right.

b. What is the marginal cost of manufacturing a tricycle.
I derived y and got (25x^1/2)/(y^1/2) +20 again I dont know what to do next

c. What is the marginal cost of manufacturing a bicycle at a level of 10 bicycles and 10 tricycles?

d. What is the marginal cost of manufacturing a tricycle at a level of 8 bicycles and 8 tricycles?
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January 31st, 2014, 05:41 PM   #2
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Re: Marginal cost with two variables, confused.

I thought I had responded to this yesterday, but found it without a response this morning so repeated my response. Now I find no response again! Did I not post it right or did someone erase it or was this on three different boards?

Quote:
Originally Posted by nakota2k
Your weekly cost to manufacture x bicycles and y tricycles is

C(x,y)=20,000+60x+20y+50?(xy)

a. What is marginal cost of manufacturing a bicycle.
I derived x and got (25y^1/2)/x^(1/2) +60 but I dont know what to do next or if that is even right.
Yes, that is the "partial derivative of C with respect to x". Strictly speaking the "marginal cost of manufacturing a bicycle" is the cost of manufacturing "one more bicycle", C(x+ 1, y)- C(x, y). For "large x", that can be approximated by

Quote:
b. What is the marginal cost of manufacturing a tricycle.
I derived y and got (25x^1/2)/(y^1/2) +20 again I dont know what to do next

c. What is the marginal cost of manufacturing a bicycle at a level of 10 bicycles and 10 tricycles?
Again, the exact value is C(11, 10)- C(10, 10) but that can be approximated by evaluated at x= 10, y= 10.

Quote:
d. What is the marginal cost of manufacturing a tricycle at a level of 8 bicycles and 8 tricycles?
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January 31st, 2014, 06:31 PM   #3
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Re: Marginal cost with two variables, confused.

@HallsofIvy: There's no record of such a deletion here (sitewide, from yesterday on).
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February 1st, 2014, 04:18 AM   #4
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Re: Marginal cost with two variables, confused.

So, my mind is going! Knew it would happen sooner or later.
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