Problem $2($Textbook Problem $9\mathrm{.}3-2)(25$ pts$.)$

Four cargo ships will be used for shipping goods from one port to four other ports $($labeled $1,2,3,4).$

Any ship can be used for making any one of these four trips. However, because of differences in the ships

and cargoes, the total cost $($in $$)$ of loading, transporting, and unloading the goods for the different

ship$-$port combinations varies considerably, as shown in the following table:

Ship v$.$ Port $1234$

$1500400600700$

$2600600700500$

$3700500700600$

$4500400600600$

The objective is to assign the four ships to four different ports in such a way as to minimize the total

cost for all four shipments.

$1.$ Formulate this problem as an assignment problem.

$2.$ Find the optimal solution using AMPL.

$3.$ Apply the Hungarian algorithm to solve this problem. Compare the results obtained in $2$ and

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