I Help me solve this chemical engineering NLP optimization problem, All you have to do is write me what to paste in Gams. QUESTIONProblem $4(1\mathrm{.}5$ points$).$

Three columns of equal height $(1m)$ and different diameter are available, with values of

$0\mathrm{.}65m,0\mathrm{.}5m,$ and $0\mathrm{.}4m,$ respectively. Determine the minimum available space

$($perimeter$)$ in the plant for their placement. Below I have provioded the expected explanation $,$ that you have to develop into gams codeApproach $1\_$ Erom Class Example

Diagram

Problem Setup

Objective: Arrange three cylindrical columns with diameters of $0\mathrm{.}4m,$

$0\mathrm{.}5m,$ and $0\mathrm{.}65m,$ respectively, within a rectangle to minimize the

perimeter of that rectangle.

Two possible objective functions: Minimize $($A$+$B$)$ and the other using

Minimize $2($A$+$B$).$ Both approaches will use the same set of variables

and constraints but will differ slightly in the objective function to illustrate

the different emphasis each approach brings.

General Setup for Both Approaches

Decision Variables

$x_i$ : $x-$coordinate of the center of the ith cylinder nd $Y_i$:$y-$coordinate of the

center of the th cylinder. Hence $($X $\{$:$x_1,Y_1)$;$(x_2,Y_2)$;$(x_3,Y_3).$

Rectangle Dimensions $-$ A: Length of the rectangle &B: Width of the

rectangle.Constraints

Non$-$overlapping Constraints

The distance between the centers of any two cylinders must be greater

than or equal to the sum of their radii:

For Cylinder $1$ and $2-(x1-x2{)}^2+(Y1-Y2{)}^2=(R1+R2{)}^2$

For Cylinder $1$ and $3-(x1-x3{)}^2+(Y1-Y3{)}^2=(R1+R3{)}^2$

$,($

For Cylinder $2$ and $3-(x2-x3{)}^2+(Y2-Y3{)}^2=(R2+R3{)}^2$

Cylinder Position

For each cylinder to be fully inside the box, we have the following constraints:

For cylinder $1$

$x_1{Y}_1{R}_1$;$x_{1}B-R_1$;$Y_{1}A-R_1$

For cylinder $2$

$x_2,Y_2{R}_2$ and $x_{2}B-R2$;$Y_{2}A-R_2$

For cylinder $3$ :

$x_3,y_3{R}_3{x}_{3}B-R_3{Y}_{3}A-R_3$

$x1,x2,x3Y1,Y2,Y3,A$;$B0$Approach $1\_$ Erom Class Example

Diagram

Problem Setup

Objective: Arrange three cylindrical columns with diameters of $0\mathrm{.}4m,$

$0\mathrm{.}5m,$ and $0\mathrm{.}65m,$ respectively, within a rectangle to minimize the

perimeter of that rectangle.

Two possible objective functions: Minimize $($A$+$B$)$ and the other using

Minimize $2($A$+$B$).$ Both approaches will use the same set of variables

and constraints but will differ slightly in the objective function to illustrate

the different emphasis each approach brings.

General Setup for Both Approaches

Decision Variables

$x_i$ : $x-$coordinate of the center of the ith cylinder nd $Y_i$:$y-$coordinate of the

center of the th cylinder. Hence $($X $\{$:$x_1,Y_1)$;$(x_2,Y_2)$;$(x_3,Y_3).$

Rectangle Dimensions $-$ A: Length of the rectangle &B: Width of the

rectangle.