Calculate the Minkowski distances between the points $(2,6)$ & $(7,$ last digit of $3769660)$ for parameters p $=1$ & p $=2.$

$$For the four given points $(0,2),(8,0),(6,3),$ & $(3,4),$ formulate the unconstrained and unweighted optimization problem that finds the point $($x$,$ y$)$ that minimizes the sum of Euclidean distances between this point & all four given points.$$

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Write the problem in LINGO style & solve it with the program. Attach the LINGO formulation & the solution.$$

What if the point must also be located in the rectangle spanned by the points $(0,0),(4,0),(0,1),$ & $(4,1)?$

Somebody claims that the weighted problem with some unspecified positive weights associated with each of the four points results in the optimal solution point $(7,4).$ Any comment?