The corner points of the feasible region of a Linear Programming Problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). If \(Z=ax+by;\) (a, \(b>0)\) be the objective function, and maximum value of Z is obtained at (0, 2) and (3, 0), then the relation between a and b is:

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

For a Linear Programming Problem (LPP), the given objective function is \(Z=x+2y\). The feasible region PQRS determined by the set of constraints is shown as a shaded region in the graph. \(P\equiv(\frac{3}{13},\frac{24}{13})\) \(Q\equiv(\frac{3}{2},\frac{15}{4})\) \(R\equiv(\frac{7}{2},\frac{3}{4})\) \(S\equiv(\frac{18}{7},\frac{2}{7})\). Which of the following statements is correct?

The number of feasible solutions of the linear programming problem given as Maximize $z=15x+30y$ subject to constraints : $3x+y\le12, x+2y\le10, x\ge0, y\ge0$ is

Solve the following Linear Programming Problem graphically: Maximise $Z=600x+400y$ subject to the constraints $x+2y\le12$, $2x+y\le12$, $4x+5y\ge20$, $x, y\ge0$