Given the quadratic programming problem \begin{align*} min \quad 0.5(x_1-a)^2+0.5(x_2-b)^2+0.5(x_3-c)^2\\ s.t \quad 4x_1+5x_2=20\\ 8x_1+3x_2+12x_3=24 \end{align*} Use the method of projection to obtain analytically the optimal solution in terms of $a,b,$ and $c$.
Can anyone help me how to figure this out? Any help or even a hint is highly appreciated. Thanks.