Express these extreme points along with their respective

Question

You need the solution to:

Suppose that a firm seeks to maximize revenue, R = 5x₁ + 4x₂, by choosing to produce quantities of two goods, x₁ and x₂, subject to certain linear production constraints.

a) These production constraints represent respectively the constraints linked to labour, capital, and raw resources required to produce quantities x₁ and x₂:

2x₁ + x₂ = 13

3x₁ + 5x₂ = 30

4x₁ + x₂ = 24.

with x₁ = 0, x₂ = 0.

b) Represent this linear programming problem in matrix form, transforming in the process the inequality constraints into equality constraints by the addition of slack variables, s₁, s₂ and s₃.

Then, utilizing the values of your extreme points found in a), find the corresponding values of the slack variables in each case.

Finally, express these extreme points along with their respective values of the slack variables as vectors in a five-dimensional space (i.e. 5 × 1 vectors).

How many non-zero elementsdo you find in each, and how do you explain this result?