# Solving A Linear Programming Problem

Otherwise, you may proceed algebraically also if the optimum point is at the intersection of two constraint lines and find it by solving a set of simultaneous linear equations.The Optimum Point gives you the values of the decision variables necessary to optimize the objective function.

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The graph must be constructed in ‘n’ dimensions, where ‘n’ is the number of decision variables.

This should give you an idea about the complexity of this step if the number of decision variables increases.

One must know that one cannot imagine more than 3-dimensions anyway!

The constraint lines can be constructed by joining the horizontal and vertical intercepts found from each constraint equation.

To find out the optimized objective function, one can simply put in the values of these parameters in the equation of the objective function. Worried about the execution of this seemingly long algorithm? Question: A health-conscious family wants to have a very well controlled vitamin C-rich mixed fruit-breakfast which is a good source of dietary fibre as well; in the form of 5 fruit servings per day.

They choose apples and bananas as their target fruits, which can be purchased from an online vendor in bulk at a reasonable price.

Now begin from the far corner of the graph and tend to slide it towards the origin. Once you locate the optimum point, you’ll need to find its coordinates.

This can be done by drawing two perpendicular lines from the point onto the coordinate axes and noting down the coordinates.

This is used to determine the domain of the available space, which can result in a feasible solution. A simple method is to put the coordinates of the origin (0,0) in the problem and determine whether the objective function takes on a physical solution or not.

If yes, then the side of the constraint lines on which the origin lies is the valid side. The feasible solution region on the graph is the one which is satisfied by all the constraints.

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