One of Speedy Airlines$$ flights is about to take off from Seattle for a nonstop flight

to London. There is some flexibility in choosing the precise route to be taken,

depending upon weather conditions. The following network depicts the possible

routes under consideration, where S and L are Seattle and London, respectively,

and the other nodes represent various intermediate locations.

$1)$ Solve the problem by using the simplex method in tabular form.

$2)$ If the objective function is changed to maximize z$=2$x$1+3$x$2+5$x$3,$ find the new

optimal solution through sensitivity analysis.

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Cost per advertisement $ $2,000$ $ $600$ $ $300$

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The winds along each arc greatly affect the flying time $($and so the fuel

consumption$).$ Based on current meteorological reports, the flying times $($in hours$)$

for this particular flight are shown next to the arcs. Because the fuel consumed is

so expensive, the management of Speedy Airlines has established a policy of

choosing the route that minimizes the total flight time. Use the algorithm to solve

this shortest$-$path problem.