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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the values of x and y that minimize the objective function P=3x+2y for the graph. What is the maximum value
Transcribed Image Text:The provided image is a graph on a coordinate plane, showing a shaded triangular region. Below is a detailed description of its elements:
### Graph Description:
- The graph represents a section of the coordinate plane with axes labeled as \( x \) (horizontal axis) and \( y \) (vertical axis).
- The grid is divided into unit squares, with the x-axis and y-axis both ranging from 0 to 10.
### Points on the Graph:
- **Point (0, 8):** This point lies on the y-axis, at the intersection of \( x = 0 \) and \( y = 8 \).
- **Point (9, 0):** Located on the x-axis, at the intersection of \( x = 9 \) and \( y = 0 \).
- **Point (3, 4):** Positioned within the graph area inside the grid, at \( x = 3 \) and \( y = 4 \).
### Shaded Region:
- The shaded area forms a triangle bounded by the points (0, 8), (9, 0), and (0, 0).
- The hypotenuse of the triangle appears to be a line connecting (0, 8) to (9, 0), suggesting this is part of an inequality boundary or a defined linear region.
This graph can be used to visually represent systems of inequalities or explore concepts related to linear programming where feasible regions are determine under constraints represented by linear equations.
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