Question

You are building a rectangular doorway. The doorway must be at least 1 meter high
and at least 0.5 meters wide. It must also enclose a door with area 2.5 m2
. The
material for the sides of the doorway cost $30 per meter and the material for the top
of the doorway costs $50 per meter. The bottom of the doorway requires no material.
What is the cheapest you can build the doorway?