Respond to this ONLY if you\'re sure from your answer. Please write with proper

Question

Respond to this ONLY if you're sure from your answer. Please write with proper ENGLISH.

Discission.

After considering the lines of equal objective function value, such as the contour lines or topographical lines.

1- Why is it necessary that a linear model will have either a single maximum point (global optimum) or an infinite number of optimal points?

2-In what situations would we have an infinite number of solutions?

3-Could we ever have a finite (and greater than 1) number of globally optimal points, all with the same objective function value?

4-That is, could we have 2, or 10, or 1000 globally optimal points with a linear model?

Why or why not?

This is optimization problem

Explanation / Answer

Solution 1. If in the linear programming model the total number of variable in the objective function function is equal to the total number of constraints, then the linear programming model have only single optimal point.

And if total number of variable in the objective function is more than or less than the total number of constraint, then the LPP has infinite number of optimal points.

Solution 2.

If total number of variable in the objective function is more than or less than the total number of constraint, then the LPP has infinite number of optimal points.

Solution 3.

Yes, it is posssible when the intersection points of the constraints lies only on the x-axis.

Solution 4.

If rank of the matrix formed by the coefficients of the vatiables of the constraints is say p, then the total number of optimal solution.

total number of solution= number of variable-p

Hence, if value of (number of variable-p) is 2 or 10, or 1000 globally optimal points accurs.

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