Answered: Q 8 Find the maximum value of the…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 1SC: Find the maximum value of P=4x+3y subject to the constraints of Example 1. {x+y42x+y6x0y0

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Find the maximum value of P=4x+3y subject to the constraints of Example 1. {x+y42x+y6x0y0
Feasible RegionAll parts of this problem refer to the following feasible region and objective function. {x0xyx+2y12x+y10 P=x+4y aGraph the feasible region. bOn your graph from part a, sketch the graphs of the linear equations obtained by setting P equal to 40, 36, 32, and 28. cIf you continue to decrease the value of P, at which vertex of the feasible region will these lines first touch the feasible region? dVerify that the maximum value of P on the feasible region occurs at the vertex you chose in part c.
Feasible region all part of this problem refer to the following Feasible region and objective function. {x0xyx+2y12x+y10}P=x+4y (a) Graph the Feasible region. (b) on your graph from part(a) , sketch the graph of the linear equation obtained by (c setting P equal to 40,36,32 and 28 . (c) if you continue to decrease the value of P, at which vertex of the Feasible region will these lines first touch the Feasible region . (d) verify that the maximum value of P on the Feasible region occurs at the vertices you too chose in part(c).

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−x	+	2y	≤	100
3x	+	12y	≤	162
6x	+	2y	≤	126

Q 8 Find the maximum value of the objective function z = 19x + 28y, subject to the following constraints. (See Example 2.) −x + 2y ≤ 100 3x + 12y ≤ 162 6x + 2y ≤ 126 x ≥ 0, y ≥ 0 The maximum value is z = ____ at (x, y) = (___, ___)

Q 8 Find the maximum value of the objective function z = 19x + 28y, subject to the following constraints. (See Example 2.) −x + 2y ≤ 100 3x + 12y ≤ 162 6x + 2y ≤ 126 x ≥ 0, y ≥ 0 The maximum value is z = __ at (x, y) = (_, ___)