How To Solve Linear Programming Problems Graphically

The maximum value of the objective function is 33, and it corresponds to the values x = 3 and y = 12 (G-vertex coordinates). In Graphical method is necessary to calculate the value of the objective function at each vertex of feasible region, while the Simplex method ends when the optimum value is found.

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In simpler terms, we try to optimize (to maximize or minimize) a function denoted in linear terms and bounded by linear constraints.

Let’s try to formalize an use-case and carry it forward throughout the article.

To complicate things further, you only have 25 and 10 units of herb A and B at your disposal.

Now the question is, how many of each medicine will you create to maximize the health of the next person who walks in?

As the constraint have few variables (only ), transforming the problem into graph of lower dimension, we can visualize it as a 2D plot.

With constraints on herbs being transformed into lines, our solution now transforms into a point of intersection.Similarly, to create one unit of medicine 2, you need 4 and 1 units of herb A and B respectively.Now medicine 1 can heal a person by 25 unit of health (whatever it is) and medicine 2 by 20 units.And medicines are the only thing which can help us with it.What we are unsure of, is the amount to each medicines to create.Here it goes, As evident, the solution was optimum and similar to what we got from graphical representation.Moving forward from this basic example, the true potential of optimization is showcased when we try to solve real world complex problems.Linear programming is the technique used to maximize or minimize a function.The idea is to optimize a complex function by best representing them with linear relationships.The point of intersection, as obvious, from the plot is (3, 4), which says, If we create 3 units of medicine 1 and 4 units of medicine 2, considering the constraints on herbs, we are best equipped to heal the next patient.Intuitively, we wanted to find a solution which satisfy all of our constraints.


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