Linear Programming

The corner points of the feasible region determined by the following system of linear inequalities \( 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 \) are \( (0,0),(5,0),(3,4) \) and \( (0,5) \). Let \( Z=p x+q y \), where \( p, q>0 \). Condition on \( p \) and \( q \), so that the maximum of \( Z \) occurs at both \( (3,4) \) and \( (0,5) \), is

The corner points of the feasible region determined by the following system of linear inequalities \( 2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0 \) are \( (0,0),(5,0),(3,4) \) and \( (0,5) \). Let \( Z=p x+q y \), where \( p, q>0 \). Condition on \( p \) and \( q \), so that the maximum of \( Z \) occurs at both \( (3,4) \) and \( (0,5) \), is

If the number of available constraints is 3 and the number of parameters to be optimised is 4 , then

If the number of available constraints is 3 and the number of parameters to be optimised is 4 , then