A small machine shop has four machines located at coordinates P$1(8,20),$ P$2(10,10),$ P$3(16,30),$ and P$4(30,10),$ Two new machines are to be located in the shop. Item movement is rectilinear. It is anticipated that there will be four trips per day between the new machines. The number of trips per day between each new machine and existing. machine is given below.

Existing Machine

$1$

$2$

$3$

$4$

New Machine

$1$

$8$

$6$

$5$

$4$

$2$

$2$

$3$

$4$

$6$

Determine the optimum locations for the new machines