In real life, we are subject to constraints or conditions.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
We only have so much money for expenses; there is only so much space available; there is only so much time.
So this means we need to find a way of using these limitations to our advantage, like finding the optimum amount of money, space, time, etc., to accomplish our goals.
And this is what linear programming is all about!
So what is linear programming?
Nothing more than taking several linear inequalities that all relate to some situation, and finding the “best” value under the given conditions.
How do we do this?
First, we must identify all constraints, by creating a system of inequalities.
Then we must identify the Objective Function, which is the equation we want to maximize or minimize.
Next, we will graph the system of inequalities and find the feasible solution, which is the shaded or overlapping region common to all conditions.
Then we will locate all vertices and corners of this feasible solution, as Purple Math accurately states.
Why?
Because the Fundamental Theorem of Linear Programming says that the optimum value always occurs at the corners or vertices of the enclosed shaded region!
Example of How to Solve using the Techniques of Linear Programming
Finally, we substitute these ordered pairs into our objective equations and select the maximum or minimum value, based on the desired result.
Additionally, we will utilize all of our skills of solving system of equations, such as the graphing method, substitution method, and the elimination method to aid us in solving linear programming word problems.
And together we will look at seven linear programming examples, each increasing in level of difficulty, so that you will feel confident in solving any linear programming problem.
Linear Programming (How-To) – Video
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