Linear Programm...

$$\displaystyle 3y-2x\ge -12$$
$$\displaystyle 2x+5y\le 20$$
The area of the triangle formed in the xy plane by the system of inequalities above is:

$$n^2 > 10$$, and n is a positive integer.

Minimize : $$z=3x+y$$, subject to $$2x+3y\le 6, x+y \ge 1, x\ge 0, y\ge 0$$

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has $$30$$ workers (male and female) and $$17$$ units capital; which he uses to produce two types of goods $$A$$ and $$B$$. To produce one unit of $$A$$, $$2$$ workers and $$3$$ units of capital are required while $$3$$ workers and $$1$$ unit of capital is required to produce one unit of $$B$$. If $$A$$ and $$B$$ are priced at $$Rs.\  100$$ and $$Rs.\ 120$$ per unit respectively, how should he use his resources to maximise the total revenue? Form the LPP and solve graphically.
Do you agree with this view of the manufacturer that men and women workers are equally efficient and so should be paid at the same rate?

If $$x+y \leq 2, x\leq 0, y\leq 0$$ the point at which maximum value of $$3x+2y$$ attained will be.

In figure 32, the shaded region within the triangle is the intersection of the sets of ordered pairs described by which of the following inequalities?

The linear programming problem:
Maximize $$z={ x }_{ 1 }+{ x }_{ 2 }$$
Subject to constraints
$$\quad { x }_{ 1 }+2{ x }_{ 2 }\le 2000,{ x }_{ 1 }+{ x }_{ 2 }\le 1500,\quad { x }_{ 2 }\le 600,\quad { x }_{ 1 }\ge 0$$

Solve the following LPP graphically. Maximize or minimize $$Z = 3x + 5y$$ subject to
$$3x - 4y \geq -12$$
$$2x - y + 2\geq 0$$
$$2x + 3y - 12\geq 0$$
$$0 \leq x \leq 4$$
$$y \geq 2$$.

Let $$P(-1, 0), Q(0, 0)$$ and $$R(3, 3\sqrt{3})$$ be three points. The equation of the bisector of the angle PQR is?

Use graph paper for this question: