What are the economic and environmental costs and benefits of using the electric dishwasher?

This also includes its manufacture and disposal. I also have to "discuss the economic and environmental costs and benefits of washing the dishes by hand."
This is a free response question for AP Environmental Science. I already did calculations to find that washing dishes by hand actually requires more energy (in BTU’s) than washing dishes using the electric dishwasher.
Here is my thesis statement: Although many people believe the electric dishwasher uses more energy than washing the dishes by hand, it is much more energy efficient to wash dishes using an electric dishwasher.

You’re correct, an energy efficient dishwasher generally uses less water and less energy than a typical hand-washer, although if you’re obsessive about washing dishes with a minimum of energy it is possible to beat the dishwasher in water and energy use. Of course, you’ll be using a lot of your own time to do so.

Modern dishwashers are designed with several features that make them particularly efficient, including smart sensors to figure out when there are no longer large Food particles in the water (‘Smart Wash’), heater in the dishwasher to heat the water to a higher temperature, which requires less soap and washes more effectively, allowing you to lower the temperature in your hot water heater to a more efficient and safer temperature; and ability to wash dishes that start off extremely dirty, so you don’t have to prerinse anything but the filthiest dishes.

A study done in the EU (described in the article linked below) found that most people used more hot water and/or soap than a typical dishwasher, when given a standard set of dishes to wash.