Linear Programm...

Convex set: A set of point in a plane is said to be convex set it the line segment joining any two points in the set, completely lies in the set.
Which of the following sets represent the convex sets ? jistify your answer.

The feasible region of an LPP is shown in the figure. If $$z=3x+9y$$, then the minimum value of z occurs at?

For the LPP; maximise $$z=x+4y$$ subject to the constraints $$x+2y\leq 2$$, $$x+2y\geq 8$$, $$x, y\geq 0$$.

If $$ 2x - y +1 = 0 $$ is tangent to the hyperbola $$ \frac {x^2}{a^2} - \frac {y^2}{16} = 1 $$ then which of the following CANNOT be sides of a right angled triangle?

The maximum value of $$z=9x+11y$$ subject to $$3x+2y\leq 12, 2x+3y\leq 12$$, $$x\geq 0, y\geq 0$$ is _________.

The minimum value of $$z=10x+25y$$ subject to $$0\leq x\leq 3, 0\leq y\leq 3, x+y\geq 5$$ is?

Two towns A and B are 60 km  apart. A school is to built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school be built at              

The feasible solution for a LPP is shown in Fig. Let $$Z = 3x - 4y$$ be the 
Objective function, Minimum of Z occurs at