Q$3)-$ From the optimal solution tableau of $(Q_2)$ find,

$($a$)$ The status of each resource.

$($b$)$ The unit worth of each resource:

$($c$)$ The maximum range of charnge in the availability of the second resource that will keep the current solution feasible.

$($d$)$ In part $($c$),$ determine the associated change in the optimal value of $Z$

Q$4)-$ Determine the starting feasible solution for the following transportation problem using the North$-$west corner rule and the least cost method, compare the results

$\backslash$table$[[,,1,\backslash$table$[[$Warchouse$],[2]],3,$Supply$],[$Factory$,1,19,21,12,30],[\backslash$table$[[2],[3]],\frac{19}{30},16,09,40],[4,15,\frac{5}{9},\frac{16}{4},50],[$Demand$,,60,\frac{9}{50},\frac{4}{55},45]]$

Q$5)-$ The following table shows the millage of the feasible links connecting seven offshore natural$-$gas wellheads with an on shore delivery point. Since the location of wellhead $1$ is the closest to shore, it is equipped with sufficient pumping and storage capacity to pump the output of the remaining six wells to the delivery point. Determine pipeline network linking all the wellheads to the delivery point that will minimize the total pipeline millage.

$\backslash$table$[[$Wellhead$,1,2,3,4,5,6,7],[1,,20,13,19,7,,],[2,15,,,4,12,,],[3,10,,,,3,,12],[4,9,4,,,11,8,],[5,7,12,3,11,,2,4],[6,,,,8,2,,9],[7,,,12,,4,9,]]$