a rectangular fence is constructed that will enclose 100 ft sq of land. three sides will be built from fencing that costs 10 dollars per foot and the 4th side will be built from fencing that costs 23 dollars per foot. find the dimensions of the rectangular fence that minimizes the cost of materials

Answer 1

x by y

x y = 100

23 x + 10 x + 20 y = cost = c

33 x + 20 y = c

y = 100/x
so
33x + 2000/x = c

dc/dx = 0 for min = 33 -2000/x^2

33 x^2 = 2000
x^2 = 60.6
x = 7.785 ft
y = 12.845 ft