For a convex quadratic programming problem with the quadratic objective and linear inequality constraints. Theoretically, we can solve them using the KKT condition to get the exact solutions. For example, consider the following problem: $$ \text{Max}\ 3x_1-(x_1-1)^2+3x_2-(x_2-2)^2 \\ \text{s.t.}\ 4x_1+x_2\leq20\\ x_1+4x_2\leq 20\\ x_1,x_2\geq 0. $$ We can easily use the KKT condition and get the exact result $x_1=2.5$ and $x_2=3.5$. I consider if we have a large-scale problem with the following format: $$ \text{min}\ x^T A X + c^Tx \\ \text{s.t.}\ Qx\leq b \\ x\geq0 $$ where A is a $n\times n$ positive definite matrix and Q is a $m\times n$ matrix ($m\geq n$). Analytically, I think I can get the exact solution (global optimum) using the KKT condition (or some other method, like the simplex method). But in tutorials, it said that it is very "expensive" to do so. Instead, we use some numerical methods to solve them, usually, we set some tolerance for the objective function (for example, $10^{-6}$).
My question is, how expensive it is if we want to get the exact solution (global optimum) of the quadratic programming problem I mentioned before? And how it relates to $n$ and $m$? Is it impossible to calculate it even with computers? I will really appreciate it if you can offer some references for this problem.