Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs, simplex method and algorithm, duality, etc.?
This does not directly address your question (and so is not an answer). But I consult this textbook when touching upon linear programming when teaching Algorithms, and I find it an impressive, unusually concise (~200 pages) text.
"The book is an introductory textbook mainly for students of computer science and mathematics."
The Klee-Minty cube (p.76).
I especially appreciate the authors connecting the linear algebra to geometry.
A simple Google search (linear programming problems and solutions textbook) yields this result as the first hit:
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. An alternate approach is to use the first six chapters of the Schaum's Outline on Operations Research (looking at the table of contents, viewable on line using the "see inside" feature at Amazon, shows they cover your topics).
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.