# Consider the following system of linear inequalities. 3x+4y <=12 4x+3y <= 12 x >= 0 y >= 0 graph, shade and find corner points.

Question
Consider the following system of linear inequalities.
$$\displaystyle{3}{x}+{4}{y}\le{12}$$
$$\displaystyle{4}{x}+{3}{y}\le{12}$$
$$\displaystyle{x}\ge{0}$$
$$\displaystyle{y}\ge{0}$$
graph, shade and find corner points.

2021-02-26
Graph the inequalities using inequality sign:

### Relevant Questions

An objective function and a system of linear inequalities representing constraints are given.
a. Graph the system of inequalities representing the constraints.
b. Find the value of the objective function at each corner of the graphed region.
c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.
$$\displaystyle{z}={2}{x}+{3}{y}$$
$$\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}$$
List all four corner points, as ordered pairs of the form ( x, y), for the following system of inequalities:
$$\displaystyle{5}{x}−{y}\le{20}$$
$$\displaystyle−{x}+{3}{y}\le{24}$$
$$\displaystyle{x}\ge{0}$$
$$\displaystyle{y}\le{0}$$
Graph the Inequalities, and shade the feasible region
$$\displaystyle{4}{x}+{5}{y}\ge{12}$$
$$\displaystyle-{x}+{2}{y}\ge{2}$$
Graph the solution set of the inequality or system of inequalities.
$$\displaystyle{\left\lbrace\begin{array}{c} {x}\ge{0}{\quad\text{and}\quad}{y}\ge{0}\\{3}{x}+{y}\le{9}\\{2}{x}+{3}{y}\ge{6}\end{array}\right.}$$
Graph the solution set of system of inequalities:
$$\displaystyle{x}\ge{0},{y}\ge{0},{3}{x}+{y}\le{9},{2}{x}+{3}{y}\ge{6}$$
Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points (if any).
$$\displaystyle{x}+{y}\ge{5}{\left({1}\right)}$$
$$\displaystyle{x}\le{10}{\left({2}\right)}$$
$$\displaystyle{y}\le{5}{\left({3}\right)}$$
$$\displaystyle{x},{y}\ge{0}{\left({4}\right)}$$
Consider the following system of linear equations:
4x+2y=25
4x-y=-5
If the value of y is 10 what is the value of X for this system:
1.1.25
2.11.25
3.1.45
4.5
$$\displaystyle{x}\ge{3}$$
$$\displaystyle{y}\ge-{1}$$