The corner points of the bounded feasible region determined by the system of linear constraints are $(0, 0)$, $(5, 0)$, $(6, 5)$, $(6, 8)$, $(4, 10)$, $(0, 8)$. Let $Z = 3x - 4y$ be the objective function. The minimum value of Z occurs at

In a linear programming problem, the constraints on decision variables $x$ and $y$ are $y-2x \leq 0$, $y \geq 0$, $0 \leq x \leq 5$. The feasible region of the above problem:

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

The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints

$x + y \leq 2$, $x \geq 0$, $y \geq 0$. Then max (z) $-$ min (z) is equal to

The feasible region represented by the constraints: $x + 2y \geq 100$, $2x - y \leq 0$, $2x + y \leq 200$, $x \geq 0$, $y \geq 0$ of an LPP is:

For a LPP, the objective function is $z=4x+3y$ and the feasible region determined by a set of linear constraints is shown in the graph as a shaded portion. Which one of the following statement is true ?

The point which provides the optimal solution of the linear programming problem

maximize $z = 21x + 35y$

$3x + 2y \leq 30$

$4x + 5y \leq 60$

$x \geq 0, y \geq 0$

has the coordinates