Question

If the garden is to be 2450 square feet, and the fence along the driveway costs $6 per foot while on the other three sides it costs only $2 per foot, find the dimensions that will minimize the cost.

Answer 1

Cost (C) = 8x + 4y
For minimum cost C' = 0
8 + 4dy/dx = 0
dy/dx = -2

d(xy)/dx
xdy/dx + y
dy/dx = -y/x = -2
y = 2x

x(2x) = 2450
2x^2 = 2450
x^2 = 1225
x = √1225 = 35
y = 2(35) = 70

Therefroe for minimum cost the dimension of the graden should be 35 by 70 feet.