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anonymous
 one year ago
I have problems with question in supplemental problem set 2. In, F3 the product of the intercepts are D = c^3/(ab) where c = 12ab and where z = ax + by + c.
The partial derivative of D with respect to a I found to be b(b4a1)(12ab)^2 =0 and the derivative of D with respect to b I found to be a(2a2b1)(12ab)^2 = 0. How do I proceed to find out the values of a, b and c that give the minimum product of the intercepts?
anonymous
 one year ago
I have problems with question in supplemental problem set 2. In, F3 the product of the intercepts are D = c^3/(ab) where c = 12ab and where z = ax + by + c. The partial derivative of D with respect to a I found to be b(b4a1)(12ab)^2 =0 and the derivative of D with respect to b I found to be a(2a2b1)(12ab)^2 = 0. How do I proceed to find out the values of a, b and c that give the minimum product of the intercepts?

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IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0would like to help but have no access to original question

phi
 one year ago
Best ResponseYou've already chosen the best response.0In the form z= ax + by+ c the (stipulated positive) intercepts on the 3 axes occur at c, c/a, c/b thus c>0, a<0, b<0 we have two (ugly) equations and 2 unknowns. \[ b(b4a1)(12ab)^2 =0 \\ a(2a2b1)(12ab)^2 = 0\] a,b,c are not zero. As the (12ab) term is in both equations, having it be 0 adds no information, thus I would solve using \[ (b4a1)=0 \\(2a2b1) = 0\] and along with \[ c = 12ab \] we can solve for a, b, and c in z= ax + by+ c that minimize the the product of the intercepts.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I did that as well, and my answer is a = 1/2 b = 1 and c = 3. Using Lagrange multipliers, I arrive at the same answer. Thanks!
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