Solving A Linear Programming Problem

It will clearly be a straight line since we are dealing with linear equations here.One must be sure to draw it differently from the constraint lines to avoid confusion.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.

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Imagine that you work for a company that builds computers.How much fruit servings would the family have to consume on a daily basis per person to minimize their cost?Solution: We begin step-wise with the formulation of the problem first.Bananas cost 30 rupees per dozen (6 servings) and apples cost 80 rupees per kg (8 servings).Given: 1 banana contains 8.8 mg of Vitamin C and 100-125 g of apples i.e. Every person of the family would like to have at least 20 mg of Vitamin C daily but would like to keep the intake under 60 mg.Be sure to keep the orientation of this ruler fixed in space.We only need the direction of the straight line of the objective function.Here we are going to concentrate on one of the most basic methods to handle a linear programming problem i.e. In principle, this method works for almost all different types of problems but gets more and more difficult to solve when the number of decision variables and the constraints increases. We will first discuss the steps of the algorithm: We have already understood the mathematical formulation of an LP problem in a previous section.Therefore, we’ll illustrate it in a simple case i.e. Note that this is the most crucial step as all the subsequent steps depend on our analysis here.Linear programming is one of the most common optimization techniques.It has a wide range of applications and is frequently used in operations research, industrial design, planning, and the list goes on.