Linear Programming

An inequality ($\leq$)

An inequality ($\geq$)

A linear equation ($=$)

A quadratic equation

The variable to be determined

The maximum availability of a resource

The minimum requirement of a resource

The profit per unit of resource

The decision variables can take fractional values

The total profit can be divided among partners

The constraints must be divisible by 10

The problem can be divided into smaller sub-problems

First quadrant only

First and second quadrants

Third quadrant only

All four quadrants

Simplex method

Corner point method

Origin test

Intercept method

$Z = 2x + 3y + 5$

$Z = x/y$

$Z = \sqrt{x} + y$

$Z = xy$

The origin only

Any random point

Corner points (vertices)

Points on the y-axis

Feasible solution

Optimal solution

Infeasible solution

Fixed solution

$(1, 0)$

$(0, 2)$

Both are equal

Cannot be determined

$(3, 0)$

$(4, 1)$

$(1, 1)$

$(2, 5)$

On the $y$-axis

On the $x$-axis

At the origin

In the interior

$x + y \le 10$

$x^2 + y \ge 5$

$2x - 3y < 7$

$y \ge 0$