Solve the following optimization problem using algebraic methods. Maximise f(x1,x2)=3x1+2x2 subjectto: x1 + x2 ≤ 5, −x1 + 2x2 ≤ 4, x1,x2 ≥0. In your answer you must: Write down the initial augmented matrix and the subsequent ma- trices from which you obtain the basic solutions. Find all of the basic solutions. State which of the basic solutions are feasible and which are not with a reason. Show how you obtain the maximum of f.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Solve the following optimization problem using algebraic methods.
Maximise f(x1,x2)=3x1+2x2 subjectto:
x1 + x2 ≤ 5,
−x1 + 2x2 ≤ 4,
x1,x2 ≥0.
In your answer you must:
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Write down the initial augmented matrix and the subsequent ma- trices from which you obtain the basic solutions.
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Find all of the basic solutions.
-
State which of the basic solutions are feasible and which are not
with a reason.
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Show how you obtain the maximum of f.
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