Question

2) Use the function h(x,y)= as follows: 1+x2+y2+x+xy 2 2D optimization utilizing Excel · Produce a surface plot of the function Utilize Solver to find the optimum value o o 2D optimization utilizing Matlab o o o Produce a surface plot the function Produce a contour plot of the function Utilize fminsearch to find the optimum value

Answer 1

For matlab

Create a meshgrid for x and y

 [X,Y] = meshgrid(-2:0.25:2) %Create a 2-D grid with uniformily spaced x-coordinates and y-coordinates in the interval [-2,2].

F = 1 / (1 + X.^2 + Y.^2 + X. + X. * Y.)

surf(X,Y,F) %Plots the surface graph of the given function

contour(X,Y,F) % Plots the contour graph of the given function

s = fminsearch(F,1) % calculate the local minima of the function F near 1 and stores that value in s

For excel

1. create a new excel spreadsheet
2. For better understanding we will give name to the cells
3. enter x , y and z values in Column A (1 to 3)
4. Select menu item Insert -> Name -> Create
5. Click on left column then click on OK button (Now it treats row A1 as x, A2 as y and A3 as z)
6. Click on cell of z and write the function to compute (1/(x^2 + y^2 +x +x*y+1))
7. create the table data by selecting some section
8. select menu item Data -> Table -> select row input and column input cell and then ok
9. open the chart wizard
10. select surface -> specify x values -> specify y values -> finish
11. For solver
12. Select option - > Add ins -> Solver ->Solver-> Ok
13. Select Data -> Solver will pop up a window
14. Select cell objective as a cell in which you want min value and By changing the variable cell as data rows
15. choose min option
16. Add
17. Solve

The solved value is stored at a specified cell