Most people aren't going to walk up to a framed 30x40 and stick their nose against the glass. You stand back a ways, right?

Doing a little math gives me a file 3456 px wide x 2304 px high...what is that, 8 megapixels? Never mind, we'll live with it. On a wide-format inkjet printer you can get good "photo quality" images at 150 dpi. 300 gives slightly better results but also gives 4 times larger files.

In your Photoshop Image Size dialog you should have a "resample image" checkbox. Turn that off and change the short dimension to 30" which will give 76.8 dpi resolution. The long dimension will then be 45" which you'll have to reduce to 40" by cropping five inches off the ends.

Make two copies of this file and stick one away as a backup.

Call one of them "version A." Crop it to 11x14 and save.

The other is "version B." Do the following:
Step 1: turn on Resample Image and change the resolution to something really high and really weird...try 783 dpi to start.
Step 2: do a 1.1-pixel Gaussian blur.
Step 3: change the resolution to 150 dpi.
Step 4: save this file, make a copy, crop an 11x14 out of the copy, and save.

A Photoshop file is a grid of dots. Each one has a color value. If you upscale a file by a rational number - from 75 to 150, for instance - Photoshop will just take the color values of two dots, average them to get a "middling" color value and shove a dot of that new value between the two existing dots. Result: the picture looks blocky. By using these weird numbers, and putting just a slight amount of blur on the dots before downsampling, the picture will look better.

Now, take both files to the print house that will do your 30x40s and print the 11x14s on the machine that will print the big posters.

Finally, get a roll of masking tape. Tape off a 30x40 rectangle on the wall and hang the 11x14s in the middle of it. Then step back to where you'd be when you look at your pictures. I think you'll be happy with one of them.

I have the full-blown version of Photoshop. If you'd like me to set up a file for you, send me a PM and I'll see what I can do.