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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 79
6장, 문제 79

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

검증된 단계별 안내
1
Identify the feasible region defined by the constraints given in the problem (usually shown graphically or by inequalities). This region represents all possible values of \(x\) and \(y\) that satisfy the constraints.
List the corner points (vertices) of the feasible region. These points are where the constraint lines intersect and are critical because the maximum and minimum values of a linear objective function over a polygonal region occur at these vertices.
Write down the objective function \(Z = 3x + 5y\) and prepare to evaluate it at each vertex of the feasible region.
Substitute the coordinates of each vertex into the objective function \(Z = 3x + 5y\) to calculate the value of \(Z\) at those points.
Compare the values of \(Z\) obtained at each vertex to determine which is the maximum and which is the minimum value of the objective function over the feasible region.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
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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, typically to maximize or minimize its value. In this case, the function 3x + 5y represents a linear combination of variables x and y, whose values we want to optimize over a given region.
추천 영상:
6:37
Permutations of Non-Distinct Objects

Feasible Region

The feasible region is the set of all possible points (x, y) that satisfy the problem's constraints, often represented as inequalities. This region is usually a polygon or polyhedron in linear programming, and the optimal values of the objective function lie within or on the boundary of this region.
추천 영상:
2:57
Probability of Non-Mutually Exclusive Events Example

Linear Programming and Optimization

Linear programming involves finding the maximum or minimum value of a linear objective function subject to linear constraints. The optimal solution for such problems occurs at the vertices (corner points) of the feasible region, so evaluating the objective function at these points determines 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=[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 \(\end{matrix}\) \(\right\)]

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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 = 10y

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교과서 질문

Use a system of equations to solve each problem. Find an equation of the parabola y = ax2 + bx + c that passes through the points (2, 3), (-1, 0), and (-2, 2).

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교과서 질문

For each pair of matrices A and B, find (a) AB and (b) BA. See Example 7. A=[34−21],B=[605−2]A = \(\left\)[ \(\begin{matrix}\) 3 & 4 \\ -2 & 1 \(\end{matrix}\) \(\right\)], \(\quad\) B = \(\left\)[ \(\begin{matrix}\) 6 & 0 \\ 5 & -2 \(\end{matrix}\) \(\right\)]

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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

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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 \(\end{matrix}\) \(\right\)]

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