IXL - Linear programming (Precalculus practice)

Consider a linear programming problem with the following constraints and objective function,

y
≤
–
x
+
10
x
≥
0
y
≥
0

The constraints are graphed below.

What are the vertices of the feasible region?

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question

Consider a linear programming problem with the following constraints and objective function,

y
≤
–
x
+
5
x
≥
0
y
≥
0

–

The constraints are graphed below.

What are the vertices of the feasible region?

key idea

Linear programming is a method of finding the minimum or maximum value of an objective function, subject to some constraints.

The constraints are the system of inequalities that represent limitations (like limited production capacity). The solution set of the constraints is called the feasible region.

The objective function is a function whose value you want to minimize (like cost) or maximize (like profit).

These are the steps to linear programming:

Determine the constraints and the objective function.
Graph the constraints.
Find the vertices of the feasible region (the solution set). Use algebra if necessary.
Evaluate the objective function at each vertex.
Draw conclusions.

If the question asks for the vertices, you can stop after Step 3.

solution

Find the vertices of the feasible region.

The vertices are

(

)

(

)

and

(

)

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O.3Find the vertices of a solution set

A.3Evaluate functions

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