Hello, I'm having some trouble with a Queuing Networks question, not the networks but solving a system of inqualities based on the network. 1. The problem statement, all variables and given/known data I have to find the value of α that gives maximum γ, and then use the value. The system is defined by [tex]5\gamma< 1[/tex] [tex]20\gamma \alpha<1[/tex] [tex](60/0.9) \gamma (1-\alpha)<1[/tex] Now [itex]\alpha[/itex] is a probability and lies in the region [itex] 0<\alpha<1[/itex] While [itex]\gamma[/itex] is a rate and is non-zero. 2. Relevant equations 3. The attempt at a solution Now I've got so far as to put the system in this form and to solve through to find that in the region [tex] 0< \alpha ≤ 10/13, that 0 < \gamma < -3/(200(\alpha-1)) [/tex] while in the region [tex] 10/13 < \alpha <1, that 0 < \gamma < 1/(20 \alpha) [/tex] Thus the maximum value of [itex]\gamma[/itex] lies in the region [itex] \gamma < 13/200[/itex] when [itex]\alpha = 10/13 [/itex]. This much is fine, but I need to use an actual value of [itex]\gamma[/itex] in the next part of the question and I can't think how to get a [itex]\gamma = [/itex] expression. Any help would be gratefully appreciated.