Question

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’.

Answer 1

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.

Answer 2

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)