Q$2[$You are not allowed to use software to solve this problem$]$

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 INR$)$ of loading, transporting, and unloading the goods for the different ship$-$port combinations varies considerably, as shown in the following table:

Ports

$1234$

Ship $1500400600700$

$2600600700500$

$3700500700600$

$4500400600600$

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.

a$)$ Describe how this problem fits into the general format for the assignment problem.

Ans:

b$)$ Obtain an optimal solution.

Ans: a$)[$Marks $3]$

b$)[$Marks $10]$