Question

The optimal solution to the following problem is:

Max X+Y²

S.T.

X²+Y² <= 200

X-Y <= 20

3Y²-X <= 50

		X = 5.34, Y=4.29
		X = 13.37, Y=4.59
		X = 11.31, Y=3.14
		X = 13.31, Y=3.14

Answer 1

Answer: X = 13.37, Y=4.59

Explanation:

This is a nonlinear programming problem. I have used excel solver to get the solution.

The solver is an excel plug in which can be installed form excel options. After installation, it is available in the data segment of the excel sheet. Once installed and launched, the parameters can be added

Spreadsheet Model along with formula:

Adding Parameters to Solver:

1st: Enter Green highlighted cell (objective function) in the set objective field

2nd: Select Max

3rd: Enter the yellow cells (decision variables) in the by changing variable cells field

4th: In constraints, click on add, enter the blue cells in the dialogue box which appears.

On the left area (cell reference), enter the left side values, select relationships in the middle, and in the right enter the right side values of the inequality signs. Similarly, repeat for the next constraints by clicking on the add button. Then click ok to go back to the parameters part.

5th; Select GRG Nonlinear in solving method (usually selected by default)

6th: Click solve

Solution:

The solution in the yellow cells is the optimal values of X and Y (answer to the question)