Posted by **Rick** on Thursday, September 22, 2011 at 5:29pm.

Given the following LP model (represented abstractly with decision variables X and Y), find the optimal solution using the ‘graphing’ approach.

Minimize 5X + 2Y

Subject to: 4X + 2Y >= 80

3X + 4Y <= 132

X + 3Y >= 45

2X - Y >= 0

And non-negativity, of course.

Your solution MUST show the following:

1) Graph

a. Plotting all 4 constraints

b. Shading in the feasible region of the entire LP model

c. Identification of the relevant extreme points

2) Relevant Extreme Points

a. Calculate the (X,Y) values of each relevant Extreme Point

b. Show the algebraic calculations of how the (X,Y) values of the Extreme Points were calculated (eyeballing a picture is not sufficient).

3) Optimal Solution

a. Evaluate each Extreme Point by the objective function

b. Identify which extreme point is the ‘best’.

- Math -
**MathMate**, Sunday, September 25, 2011 at 1:05pm
First (probably on paper), plot all the lines that represent constraints (3 explicit constraints

4X + 2Y >= 80

3X + 4Y <= 132

X + 3Y >= 45

2X - Y >= 0

plus x≥0 and y≥0.

Form a convex polygon bounded by the 6 lines, and identify the coordinates of all the vertices (extreme points).

Follow instruction #2 and complete the problem as required.

If you encounter difficulties, post again.

- Math -
**MathMate**, Sunday, September 25, 2011 at 1:05pm
First (probably on paper), plot all the lines that represent constraints (3 explicit constraints

4X + 2Y >= 80

3X + 4Y <= 132

X + 3Y >= 45

2X - Y >= 0

plus x≥0 and y≥0.

Form a convex polygon bounded by the 6 lines, and identify the coordinates of all the vertices (extreme points).

Follow instruction #2 and complete the problem as required.

If you encounter difficulties, post again (as a follow-up to this post)

## Answer this Question

## Related Questions

Quantitative methods - Missouri Mineral Products (MMP) purchases two unprocessed...

Math - Which term best describes the solution of the situation represented by ...

math - Four key marketing decision variables are price (P), advertising (A), ...

applied statistics - Discuss how the General Linear Model assigns the optimal “...

math - An ad campaign for a new snack chip will be conducted in a limited ...

Statistics - General Linear Model How does the general linear model assign ...

Systen of Equalities - Which term best describes the solution of the situation ...

Maths - In the following problems, Θ = 20 + units digit of your day of ...

math - find the equations of the quadratics given the following information ...

math - Maximize P = 4x + 20y subject to these constraints: 2x + 15y ≤ 700 ...