I posted the whole question to give some context, but my problem lies with (iv). I think you're meant to use a formula for the generalization of the optimal solution, but I'm not really sure what this means or how to apply it. I have looked online but I cant seem to find anything that relates to this.
I know the two extreme optimal solutions are $\left(\frac{3}{7},\frac{24}{7},\frac{22}{7}\right)$ and $\left(\frac{12}{5},\frac{4}{5},\frac{46}{5}\right)$ and I understand that graphically $\left(1,\frac{8}{3}\right)$ will be on the line between them. I just do not understand the algebra on how to prove it.
Any help I'll be grateful.