Consider the linear program

minimize subject to

$$

Ax b

in which

$3-1$

$2$

$15$

$2$

$45$

$0$

$8$

A

b $=$

C$=$

$-6$

$9$

$5$

$13$

$1$

$1$

$1$

$4$

Use the optimality criteria $($see page $127)$ to decide whether or not $\backslash$sigma $=(2,0,5)$ 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.$]$