The variables x, y, and z can take only positive values and are such that z=3x+2y and xy=600. Show that z=3x + 1200/x, then find the stationary value of z and determine its nature.
Please help me solve this, 10 points??
Please help me solve this, 10 points??
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Differentiate z wrt x
z=3x+1200x^-1
dz/dx= 3-1200x^-2, at a stationairy point dz/dx=0 so
3=1200/x^2, so x^2=400
x=+20, x=-20 BUT X CANNN'T BE NEGATIVE SO ONLY X=20 EXISTS.
diff, wrt again
d2z/dx2= 2400x^-3, now if x>0, the the 2nd derivative is a local minimumj as it'll be greater than zero.
If d2x/dx2>0 local minimum
z=3x+1200x^-1
dz/dx= 3-1200x^-2, at a stationairy point dz/dx=0 so
3=1200/x^2, so x^2=400
x=+20, x=-20 BUT X CANNN'T BE NEGATIVE SO ONLY X=20 EXISTS.
diff, wrt again
d2z/dx2= 2400x^-3, now if x>0, the the 2nd derivative is a local minimumj as it'll be greater than zero.
If d2x/dx2>0 local minimum