For a two variables linear programming problem (LPP), which of the following statement is correct ?

The minimum value of the objective function $z = x + 2y$ of an L.P.P. subject to constraints $2x + y \geq 3, \frac {x} {2} + 2y \geq 6, x \geq 0, y \geq 0$ is:

An objective function $z = ax + by$ is maximum at points (15,15) and (0, 20). If $a, b \geq 0$ and $ab = 27$, then the maximum value of the objective function is

A manufacturer of electronic circuit has a stock of 200 resistors, 120 transistors and 150 capacitors and is required to produce two types of circuits A and B. Type A requires 20 resistors, 10 transistors and 10 capacitors. Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type A circuit is Rs. 50 and that on type B circuit is Rs. 60, identify the constraints for this LPP, if it was assumed that x circuit B of type A and y circuits of type B was produced by the manufacturer.

A. $x + 2y \geq 15$

B. $2x + y \leq 20$

C. $x + 2y \leq 12$

D. $x, y \leq 0$

Choose the correct answer from the options given below

If the corner points of the bounded feasible region of an LPP with objective function Maximize $z = 2x + 3y$ are (0,0), (1,2) and (1,1), then its optimal value is

If corner points of the bounded feasible region of a linear programming problem are as in the figure given below and $z = px + qy$, $(p,q > 0)$ is an objective function. Then the relation between $p$ and $q$, when $z$ is maximum at $D(4,10)$ and $C(6,8)$, is:

The feasible region of a linear programming problem is bounded. The corresponding objective function is Z= 3x-4y. The objective function attains