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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Lial 13th EditionCh. 5 - Systems and Matrices문제 81
6장, 문제 81

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 10y

검증된 단계별 안내
1
Identify the feasible region and its vertices from the given graph or constraints. The maximum and minimum values of a linear objective function over a polygonal feasible region occur at the vertices (corner points) of that region.
List the coordinates of each vertex of the feasible region. These points are where the constraints intersect and define the boundary of the feasible region.
Substitute the y-coordinate of each vertex into the objective function \$10y$ to find the value of the objective function at each vertex.
Compare the values obtained from each vertex to determine which is the maximum and which is the minimum value of the objective function over the feasible region.
State the maximum and minimum values along with the corresponding points in the feasible region where these values occur.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Objective Function

An objective function is a mathematical expression that defines the goal of an optimization problem, such as maximizing or minimizing a value. In this case, the function is 10y, meaning the value depends solely on the variable y. Understanding how to evaluate this function at different points is essential for finding its maximum and minimum.
추천 영상:
6:37
Permutations of Non-Distinct Objects

Feasible Region

The feasible region is the set of all possible points that satisfy the problem's constraints, often represented graphically as a polygon or area on the coordinate plane. The maximum and minimum values of the objective function must lie within this region, so identifying and understanding its boundaries is crucial.
추천 영상:
2:57
Probability of Non-Mutually Exclusive Events Example

Optimization in Linear Programming

Optimization involves finding the highest or lowest value of the objective function within the feasible region. In linear programming, these extrema occur at the vertices (corner points) of the feasible region. Evaluating the objective function at each vertex helps determine the maximum and minimum values.
추천 영상:
06:07
Linear Inequalities
관련 실천
교과서 질문

For each pair of matrices A and B, find (a) AB and (b) BA.

A=[−101011−1−10],B=[001010100]A = \(\left\)[ \(\begin{matrix}\) -1 & 0 & 1 \\ 0 & 1 & 1 \\ -1 & -1 & 0 \(\end{matrix}\) \(\right\)], \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \(\end{matrix}\) \(\right\)]

112
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교과서 질문

For each pair of matrices A and B, find (a) AB and (b) BA. A=[0−5−42],B=[3−1−54]A = \(\left\)[ \(\begin{matrix}\) 0 & -5 \\ -4 & 2 \(\end{matrix}\) \(\right\)], \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 3 & -1 \\ -5 & 4 \(\end{matrix}\) \(\right\)]

132
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교과서 질문

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 3x + 5y

524
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교과서 질문

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

-2x - 2y + 3z = 4

5x + 7y - z = 2

2x + 2y - 3z = -4

645
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교과서 질문

Perform each operation, if possible.

[−2550143−4−1][10−1−10011−1]\(\left\)[ \(\begin{matrix}\) -2 & 5 & 5 \\ 0 & 1 & 4 \\ 3 & -4 & -1 \(\end{matrix}\) \(\right\)] \(\left\)[ \(\begin{matrix}\) 1 & 0 & -1 \\ -1 & 0 & 0 \\ 1 & 1 & -1 \(\end{matrix}\) \(\right\)]

83
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교과서 질문

For each pair of matrices A and B, find (a) AB and (b) BA. A=[01−1010001],B=[100010001]A = \(\left\)[ \(\begin{matrix}\) 0 & 1 & -1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \(\end{matrix}\) \(\right\)]

62
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