Answer Check: Optimization/minimization of cost. Rectangle plot. 3 hedges on one side, a fence on the remaining. Hedge= $45 per linear foot. Fence= $125 per linear foot.
What is the minimum cost of a plot that is 1000ft^2 in area?

My work: Minimize- p=90x+170y
constraint- 1000=xy 1000/x=y p=90x+170(1000/x)
p=90x+170000/x
p'=90-170000/x^2

0=90-170000/x^2
90=170000/x^2
x= Sqrt(170000/90)
x=(Sqrt(17000))/3
Plug that back into p=90x+170000/x
Get p=(60)(sqrt of 17000) which is approx $7,823 If you use other variable to optimize you'd get p=(600)(sqrt 170)

Question

Answer Check: Optimization/minimization of cost. Rectangle plot. 3 hedges on one side, a fence on the remaining. Hedge= $45 per linear foot. Fence= $125 per linear foot. 
What is the minimum cost of a plot that is 1000ft^2 in area? 

My work: Minimize- p=90x+170y 
constraint- 1000=xy 1000/x=y p=90x+170(1000/x) 
p=90x+170000/x 
p'=90-170000/x^2 

0=90-170000/x^2 
90=170000/x^2 
x= Sqrt(170000/90) 
x=(Sqrt(17000))/3 
Plug that back into p=90x+170000/x 
Get p=(60)(sqrt of 17000) which is approx $7,823 If you use other variable to optimize you'd get p=(600)(sqrt 170)

anonymous · Answer

Did I mess that problem up completely? haha

anonymous · Answer

sorry, lemme do that again...

anonymous · Answer

I figured you would minimize the perimeter. P=45x +45x + 45y +125y
p=90x+170y

anonymous · Answer

ok, your cost function is the same is mine. 
constraint is good.
procedure is good.
analysis is good.
everything looks good..
er go... it's good!  :)

anonymous · Answer

haha thanks! Off to class, now, take care!

anonymous · Answer

good luck np