$5-22.$ Compare the starting solutions obtained by the northwest$-$corner, least$-$cost$,$ and Vogel methods for each of the models in Table $5\mathrm{.}33.$

$5-23.$ Consider the transportation models in Table $5\mathrm{.}34.$

$($a$)$ Use the northwest$-$corner method to find the starting solution.

$($b$)$ Develop the iterations that lead to the optimum solution.