*Joanne can carry not more than 3.6 kg of fruits home.a) Write 3 inequalities to represent the information given above.*

Simplex methods visit basic solutions computed by fixing enough of the variables at their bounds to reduced the constraints \(Ax = b\) to a square system, which can be solved for unique values of the remaining variables.

Basic solutions represent extreme boundary points of the feasible region defined by \(Ax = b\), \(x = 0\), and the simplex method can be viewed as moving from one such point to another along the edges of the boundary. Barrier or interior-point methods by contrast visit points within the interior of the feasible region.

Choose the scales so that the feasible region is shown fully within the grid.

(if necessary, draft it out on a graph paper first.) Shade out all the unwanted regions and label the required region It also possible to test the vertices of the feasible region to find the minimum or maximum values, instead of using the linear objective function.

In these lessons, we will learn about linear programming and how to use linear programming to solve word problems.

Many problems in real life are concerned with obtaining the best result within given constraints.Although all linear programs can be converted to standard form, it is not usually necessary to do so to solve them.Most LP solvers can handle other forms such as There are two families of techniques in wide use today, simplex methods and barrier or interior point methods.In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost.However, there are constraints like the budget, number of workers, production capacity, space, etc.In a linear program, a variable can take on any continuous (fractional) value within its lower and upper bounds.For many applications, fractional values do not make sense.These techniques are general purpose in that they take as input an LP and determine a solution without reference to any information concerning the origin of the LP or any special structure of the LP.They are fast and reliable over a substantial range of problem sizes and applications.For more information, see Integer Linear Programming and its related pages.The importance of linear programming derives both from its many applications and from the existence of effective general purpose techniques for finding optimal solutions.

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