A simple Google search (linear programming problems and solutions) yields this result:

https://www.springer.com/gp/book/9783540417446 (Linear Optimization and Extensions:
Problems and Solutions; Authors: Alevras, Dimitris, Padberg, Manfred W.) 

This appears to be exactly what you are looking for, based on reading the intro as well as just the title itself.

Another suggestion is the first 6 chapters of the Schaum's Outline on Operations Research.

The Google search also shows that this question has been asked several times on the main (non-ed) math site.  Several other texts have been suggested.  Worth a look, although you will find many people who just suggest the text they had or who ignore the problems/solutions characteristic, a requirement for you.  Still, worth a quick look if the two previous solutions are not what you want.