The solution is to use a larger monitor.
Not meant as a "clever" reply - this is what higher resolutions are primarily meant for.
A resolution or 1024x768 is appropriate for a 17" monitor - but not for a 15" - and some people would prefer 800x600 even on a 17" monitor. If you use a resolution too high for the monitor size, then you get what you see - objects and text are too small
Normally web pages should be designed to be readily viewable properly any resolution/monitor size. I understand that you may have been given specifications as part of your course work, but you can always "think independantly", as long as you can give a justification for doing so. Any web designer should, IMHO, be primarily concerned in making pages viewable to average users on average systems - unless you have been tasked to produce a web page for a very specific audience (such as graphics designers!). Graphics designers will probably be used to working on 19-21" monitors, by the way.