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)