$5\mathrm{.}6$ Consider the linear program minimize subject to c$?$x Ax $>$ b x $>0$ in which A$=|3-12]450-69511111$ b$=1813$ ct CON Use the optimality criteria $($see page $127)$ to decide whether or not z $=(2,0,5)$ is an optimal solution of the LP$.($Hint: Assume that $$ is an optimal solution. Use the necessary conditions of optimality to determine what the vector y would have to be$.$ Check to make sure that all the conditions of optimality are met.$]$ Optimality conditions for another pair of dual linear programs A vector $$ is optimal for the linear program minimize cr subject to Ar $>$b$,$ x $>0$ if and only if there exists a vector y such that Az $>$ b$,>0($primal feasibility$)$ GTA SCT$,$ y $20($dual feasibility$)$T $($A$$ b$)=0($complementary slackness$)($TTA $$ c$")$ z $=0($complementary slackness$).$ The reasoning behind these optimality conditions is much the same as for the standard form of the LP$.$ Needless to say, we must take account of the inequality constraints in the primal and the nonnegativity of the dual variables. Under these circumstances, we get two sets of complementary slackness conditions. Here again, the positivity of variables in one problem has consequences for the constraints of the other: Ji $>0=($Az $$ b$)$; $=0$ and Z; $>03(71$A $$ c$)$; $=0.$