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Chapter 5: Problem 27

In your own words, describe how to solve a linear programming problem.

Short Answer

Expert verified
To solve a linear programming problem, formulate the problem by identifying the variables, constraints, and objective function. Plot these constraints on a graph to establish the feasible region. Determine the vertices of this region and substitute into the objective function. The vertex that optimizes this function is the solution.

Step by step solution

01

Problem Formulation

Identify and define the variables, constraints, and the objective function from the problem. The objective function is what you are trying to maximize or minimize while the constraints are the restrictions or conditions that need to be adhered to.
02

Graphical Representation

After formulating the problem, create a graph to represent the constraints. This is only feasible for linear programming problems with two variables. This graph will help illustrate the feasible region - the set of all possible solutions.
03

Determining the Vertices

Once the feasible region is identified, the next step is to find the vertices or corners of this region. These vertices are potential solutions to the problem.
04

Identifying Optimum Solution

Finally, substitute the values of the vertices in the objective function. The solution which either maximizes or minimizes (as per the problem statement) this function will be the optimal solution.

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Most popular questions from this chapter

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &x+y=6\\\ &y=2 x \end{aligned} $$

In Exercises \(19-30,\) solve each system by the addition method. \(x+y=6\) \(x-y=-2\)

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(2 x=3 y+4\) \(4 x=3-5 y\)

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(x+3 y=2\) \(3 x+9 y=6\)

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &y=\frac{1}{3} x+\frac{2}{3}\\\ &y=\frac{5}{7} x-2 \end{aligned} $$
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