Question

A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct

Answer 1

f(x) = 3(2x + 320/x) + 15(320/x)

f'(x) = 3(2 - 320/x²) - 15(320/x²) = 0

6 - 24(320/x²) = 0

24(320/x²) = 6

320/x² = 1/4

x² = 1,280

x = 16√5, 320/x = 20/√5 = 4√5

The dimensions should be 16√5 ft by 4√5 ft (about 35.78 ft by 8.94 ft).