Solve the following optimization problems and justify your solutions.

All work shown for these problems must be handwritten.

A landscape architect wishes to enclose a rectangular garden of area $1000m^2$ on one side by a brick wall and by metal frencing along the other three sides. The cost for the brick wall is $$\frac{100}{m}$ and the cost for metal fencing is $$\frac{20}{m}.$

What dimensions of the rectangle will minimize the cost of the materials, and how much would the misterials cast?