Ruciz Posted June 11, 2004 Share Posted June 11, 2004 (edited) I have been working on a calculus problem for the past little while and its making me mad. because its an easy question but I am missing something. Its a rectangle divided in half vertically, being fenced on all sides (all 5 sides) by 600 m of fencing. (A rectangular field is to be enclosed and subdivided with fencing into two areas) |---------------------|-------| |---------------------|-------| /edit - the diagram didn't work too well, but it gives a rough idea (diagram with x on vertical axis, and Y on the horizontal axis) the question is asking if 600 m of fencing is available, determine the value of x and y so that the total area is a maximum. I have derived 2 equations but don't know if they are right, or how to combine them: 3x + 2y = 600 and (X)( Y ) = A can anyone help this poor soul? thanks in advance for any advice Edited June 11, 2004 by Ruciz Link to comment Share on other sites More sharing options...
Raum Posted June 11, 2004 Share Posted June 11, 2004 Roofles. Just go smoke pot and eat spicy doritos, then kick a dog int he head and sprinkle lambchop on him. :) Link to comment Share on other sites More sharing options...
spiegel Posted June 11, 2004 Share Posted June 11, 2004 im not sure, but first get the area of each rectangle base * height then plug it into the x and y respectively then derive. again im not sure if this is right, i can do it if i write it out but......im just too lazy ;) :D Link to comment Share on other sites More sharing options...
Raum Posted June 11, 2004 Share Posted June 11, 2004 im not sure, but first get the area of each rectangle base * height then plug it into the x and y respectively then derive. again im not sure if this is right, i can do it if i write it out but......im just too lazy ;) :D Spiegeldizzle! Link to comment Share on other sites More sharing options...
spiegel Posted June 11, 2004 Share Posted June 11, 2004 Spiegeldizzle! fo shizzle? :huh: :huh: Link to comment Share on other sites More sharing options...
jsklar Posted June 11, 2004 Share Posted June 11, 2004 (X)( Y ) = AOkay ... so you need to turn this equation into a function. The area changes as x and y change, correct? and you need to maximize the value of A ...So let's make A a function of x. Take 3x + 2y = 600 and solve for y. You get (600 - 3x) / 2. Now plug that in for y in the first equation and call it a function of x.You now have A(x) = (x) * (600 - 3x) / 2. Now, to find the maximum value of the function, all you need to do is take the derivative and find a critical point at which the sign of the derivative changes from (+) to (-) - you know how to do that right? Reply again if you still need help from there... Link to comment Share on other sites More sharing options...
Ruciz Posted June 11, 2004 Author Share Posted June 11, 2004 thanks for your help :) knew right away what I done wrong and the question took right off and worked out like a breeze after that. x = (200) / 3 m and y = 200 m. Link to comment Share on other sites More sharing options...
G4M3R Posted June 11, 2004 Share Posted June 11, 2004 Roofles. Just go smoke pot and eat spicy doritos, then kick a dog int he head and sprinkle lambchop on him. :) Thats the same answer I got :D Link to comment Share on other sites More sharing options...
jsklar Posted June 11, 2004 Share Posted June 11, 2004 thanks for your help :) knew right away what I done wrong and the question took right off and worked out like a breeze after that. x = (200) / 3 m and y = 200 m. any time if theres anything i enjoy more than doing math its teaching it :) (why am i such a dork??) Link to comment Share on other sites More sharing options...
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