Using ImageMagick, how can I resize an image to have a minimum:

• height of 150px
• width of 200px

and also have a maximum:

• height of 225px
• width of 275px

UPDATE:

In case it helps, here's a further explanation of what I'm experiencing.

I have a buch of images with all different ratio dimensions. Some images have 1:5 height/width ratios. Some have 5:1 height/width ratios. So that I want to do is set that a minimum height/width size for the image but also don't want the image size to be larger than a particular size.

If I need to apply white padding to an image to make it fit within my constraint so that I don't have to distort the image, I'd like to do so.