The feasible region for an L.P.P is always a/an

The number of corner points of the feasible region of an LPP determined by the constraints $x - y \geq 0$, $2y \leq x + 2, x \geq 0, y \geq 0$ is

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

The objective function of an LPP is $z = ax + by$. If the maximum value of the objective function is 180, which occurs at two points (15,15) and (0,20), then which one of the following is true?

If the objective function $z = px + qy$ has its maximum value at the points (2, 1) and (0, 6), then the relationship between p and q is:

The feasible solution to the LPP is-

If the objective function $Z = px + qy, p > 0, q > 0$ of a linear programming problem attains its optimal value at the points (4, 7) and (5, 5) and $pq = 50$ then