Linear Programming

A factory produces two products X and Y . The profit earned by selling X and \(Y\) is represented by the objective function \(Z=5 x+7 y\), where \(x\) and \(y\) are the number of units of X and Y respectively sold. Which of the following statement is correct?

A linear programming problem deals with the optimization of a/an :

The number of corner points of the feasible region determined by constraints \(\mathrm{x} \geq 0, \mathrm{y} \geq 0, \mathrm{x}+\mathrm{y} \geq 4\) is :

A linear programming problem deals with the optimization of a/an :

The common region determined by all the constraints of a linear programming problem is called :

A factory produces two products \(X\) and \(Y\) . The profit earned by selling \(X\) and \(Y\) is represented by the objective function \(Z=5 x+7 y\), where \(x\) and \(y\) are the number of units of \(X\) and \(Y\) respectively sold. Which of the following statement is correct?

The common region determined by all the constraints of a linear programming problem is called :

Assertion (A) : Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R) : The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.