A rectangular rose garden will be surrounded by a brick wall on three sides and by a fence on the fourth side. The area of the garden will be 1000m^2. The cost of the brick wall is $192/m. The cost of the fencing is $48/m. Find the dimensions of the garden so that the cost of the materials will as low as possible

Answer 1

If the brick wall side has length x and the width is y, then
xy = 1000
The cost is
c = 192x + 48(x+2y) = 192x + 48(x + 2000/x) = 240x + 96000/x
to minimize c, we have
dc/dx = 240 - 96000/x^2
dc/dx = 0 at x=20, so the garden is 20 by 50