Platform beds are sturdy, simple bed frames that are typically low to the ground---they are seen in many Asian-style bedrooms and are particularly suited for use with futon mattresses. Commercially available platform bed frames can cost a pretty penny, so making your own is not only good for your pocket but has the advantage of being totally customisable. You don't need to be an engineering whizz to make a platform bed frame: if you know how to drill a hole and bolt things together, you're good to go.
Align the 75-inch planks around 13 inches apart, resting vertically on their 2-inch side. Abut the 40-inch planks on either end of the 75-inch planks, making sure the ends are flush and everything is at right angles.
Bolt the planks together, so that there are two bolts in the end of each 75-inch plank---6 bolts in each 40-inch plank---12 bolts in total. This is the frame of the platform bed.
Place two slats on either end of the frame, with 3/4 of an inch overhanging the frame end. Make sure they are centred on the frame---there should be around 7 1/2 inches of overhang on either side. Bolt these planks in place, 1 bolt per frame plank, which is 3 bolts in each slat.
Lay out the remaining slats, around 1/2-inch apart, then bolt them down in the same way as you bolted down the first two. The platform frame is now complete.
Paint and varnish as desired. This is a standard double-bed sized platform bed---adjust the measurements of the planks and slats according to the size bed you need.