Consider the following optimization problem:

min :

$8$x$1+12$x$2+16$x$320$x$424$x$528$x$6(1)$

s$.$t$.$ :

x$1+3$x$2+3$x$3=5(2)$

x$4+$ x$5+$ x$6<=10(3)$

$0<=$ xi $<=9$i $=1,...,6(4)$

where the variables of the multivariable optimization problem are integers. Use Extension$-2$ type

approach, $($i$.$e$.,$ Treat the multiple variables together as one structure or as one vector$).$ Answer

the following: $($d$)$ Execute $3$ full iterations of the random$-$walk search with the extended$/$expanded neighborhood.

Use starting solution as $[3,0,1,1,1,1]$T

$.$ Handle Constraint$(2)$ & $(3)$ by creating a penalized

objective function. Assume all the penalty coefficients are equal to $1000.$ Use random numbers

from the random number table. See explanation at the end of this HW for generating random

numbers.