Graph the inequalities using inequality sign:

Question

asked 2021-01-02

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.

\(\displaystyle{z}={2}{x}+{3}{y}\)

\(\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}\)

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.

\(\displaystyle{z}={2}{x}+{3}{y}\)

\(\displaystyle{\left\lbrace\begin{array}{c} {x}{\quad\text{and}\quad}{y}\ge{0}\\{2}{x}+{y}\le{8}\\{2}{x}+{3}{y}\le{12}\end{array}\right.}\)

asked 2021-01-28

List all four corner points, as ordered pairs of the form ( x, y), for the following system of inequalities:

\(\displaystyle{5}{x}−{y}\le{20}\)

\(\displaystyle−{x}+{3}{y}\le{24}\)

\(\displaystyle{x}\ge{0}\)

\(\displaystyle{y}\le{0}\)

\(\displaystyle{5}{x}−{y}\le{20}\)

\(\displaystyle−{x}+{3}{y}\le{24}\)

\(\displaystyle{x}\ge{0}\)

\(\displaystyle{y}\le{0}\)

asked 2020-10-18

Graph the Inequalities, and shade the feasible region

\(\displaystyle{4}{x}+{5}{y}\ge{12}\)

\(\displaystyle-{x}+{2}{y}\ge{2}\)

\(\displaystyle{4}{x}+{5}{y}\ge{12}\)

\(\displaystyle-{x}+{2}{y}\ge{2}\)

asked 2021-03-05

Graph the solution set of the inequality or system of inequalities.

\(\displaystyle{\left\lbrace\begin{array}{c} {x}\ge{0}{\quad\text{and}\quad}{y}\ge{0}\\{3}{x}+{y}\le{9}\\{2}{x}+{3}{y}\ge{6}\end{array}\right.}\)

\(\displaystyle{\left\lbrace\begin{array}{c} {x}\ge{0}{\quad\text{and}\quad}{y}\ge{0}\\{3}{x}+{y}\le{9}\\{2}{x}+{3}{y}\ge{6}\end{array}\right.}\)

asked 2020-12-05

Graph the solution set of system of inequalities:

\(\displaystyle{x}\ge{0},{y}\ge{0},{3}{x}+{y}\le{9},{2}{x}+{3}{y}\ge{6}\)

\(\displaystyle{x}\ge{0},{y}\ge{0},{3}{x}+{y}\le{9},{2}{x}+{3}{y}\ge{6}\)

asked 2020-12-07

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).

\(\displaystyle{x}+{y}\ge{5}{\left({1}\right)}\)

\(\displaystyle{x}\le{10}{\left({2}\right)}\)

\(\displaystyle{y}\le{5}{\left({3}\right)}\)

\(\displaystyle{x},{y}\ge{0}{\left({4}\right)}\)

\(\displaystyle{x}+{y}\ge{5}{\left({1}\right)}\)

\(\displaystyle{x}\le{10}{\left({2}\right)}\)

\(\displaystyle{y}\le{5}{\left({3}\right)}\)

\(\displaystyle{x},{y}\ge{0}{\left({4}\right)}\)

asked 2021-05-03

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

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

asked 2021-02-06

Sketch the graph of the solution of the system of linear inequlities

-3x+2y<6

x+4y>-2

2x+y<3

-3x+2y<6

x+4y>-2

2x+y<3

asked 2021-01-04

Fill in the blank/s: A system of linear inequalities is used to represent
restrictions, or ________ on a function that must be maximised or minim,ised. Use the graph of such a system of inequalities, the maximum and minimum values of the function occur at one or more of the _____________ points.

asked 2020-11-05

Graph the solution set for the system of linear inequalities

\(\displaystyle{x}\ge{3}\)

\(\displaystyle{y}\ge-{1}\)

\(\displaystyle{x}\ge{3}\)

\(\displaystyle{y}\ge-{1}\)