Write a Matlab script called yourlastname$\_8\_1.m$ which creates and plots a $2-$D array of points that represent a two dimensional shape as described below. Using the lecture example box$\_$demo$\_1.$m $($available on Monday's Brightspace site$)$ as a guide, your script must include:

A "main" function which clears the command window $($clc$),$ clears all workspace variables $($clear all$)$ and closes all open figure windows $($close all$)$; declares the variables $Nx,NY,d$ and color to be global; defines a $5050$ design space by setting $Nx=50$ and $NY=50$; initializes $NYNx$ arrays $d$ and color to false and char $(0),$ respectively.

Commands to create the following shapes:

a red circle of radius, $R=15,$ centered at $x=y=25$

a green box with $17x33$ and $17y33$

a circular hole of radius $R=5,$ centered at $x=25,y=25$

For the box, use the function box$2$D $($available in the file box$\_$demo$\_1.$m$).$ For the circles, add a new function called circle which is called using the command

function circle $($xC$,$ yc$,$ R$,$ D$,$ C$)$

where $(xC,yc)$ is the coordinate of the center of the circle, $R$ is the radius of the circle, $D$ is a logical true or false $($true to add points, false to remove points$)$ and $C$ is the desired color $(\text{'}$r$\text{'},\text{'}$g$\text{'},$ etc.$).$ Within the function, include two nested loops in which the distance from each $(x,y)$ point to the center of the circle, given by $\sqrt[\phantom{2}]{(x-x_c{)}^2+(y-y_c{)}^2},$ is computed and, if the distance is less than or equal to $R,$ the corresponding $d(i,j)$ is set to true and color$(i,j)$ is set to $C.$ Include the main program and both functions in the same file $($yourlastname$\_8\_1.$m$)$

Display the resulting shape using the plot command within two nested for loops, as done in box$\_$demo$\_1.$m