This is not exactly as cheap as possible in my opinion and many others.
Many miners don't buy a computercase to save money.
I myself buy the cheapest computercases I can get and modified the sidepanel to fit a 20 cm fan for cold air intake.
I then put a metal gauze in front of the fan to keep the components in the computercase dust free.
Once in a month all I have to do is to use a vacuum cleaner to get rid of the dust from the metal gauze.
Almost no dust inside the GPU fans and other fans in the computercases.
I remove all unnecesary slot covers from the computercase.
I mount the PSU upside down and use the PSU fan to blow air out of the computercase.
Together with the rearfan heat has no chance to build up because the intake and out take of air happens so fast.
When I finished building a rig, I turn the computercase upside down.
Why?
Heat moves upwards, but the heatpipes in the GPU point downwards.
Because of a stupid legacy from the past most of the motherboards are wrongly designed.
To correct this mistake I turn the case upside down.
You can check it out yourself with MSI Afterburner.
Look at the temps. when the computercase is in normal position and then look at the temps. when you turn the computercase upside down.(Cases most have good airflow)
Many miners have their GPU in the open air.
Their GPU are about 3 degree celsius lower then mine when they are new, but after 1 month it will be hotter than mine because dust is building up inside the fans.
My rigs stay at the same temps. and I don't have to shut down my rigs to clean the dust.
Beside dust building up in your GPU fans, electronics components have a much shorter life span than when you place it inside a computercase.
Save money and install your OS on a USB stick or disassemble a HDD from a broken computer.
The price of a 7970 will not rectify the increase of speed compare with a 7950.
Overclock the GPU core for faster speed. (This will increase power consumption)
Downclock the memory speed (Faster memory will not increase speed but will use more energy)
Undervolt your GPU (Your maximum speed will be a bit lesser but you save a lot energy)
A 7950 will do about 550-575 MH/s with some overclocking and undervolting when you are using CGminer.
Keep in mind that you want to pay off your rig as fast as you can, don't under estimate your power cost unless it is free.
Everything has to be build as cheap as possible.
When you have two 7970 and a sempron processor, your system will not use more than 480 watt if you overclock and undervolt it.
Your PSU is overkill unless you have future plans.
A good 850 watt PSU can easily handle 3 7970.
Save money on your motherboards and use pcie x1 to pcie x16 extenders.
Sorry for my bad English.
It took me a hour to write this shit.
Dutch was easier for me