Algebra Consider the constraints 2x+y ≤ 6, y-x≤ 2, y+ 1 ≥a, x, y ≥ 0. (a) Plot the constraints and shade the feasible region. In your plot, label each line which forms the boundary of the feasible region. (b) Write the feasible region in matrix-vector form Ax ≤ b, x ≥ 0. (c) Find all vertices of the feasible region.
Algebra Consider the constraints 2x+y ≤ 6, y-x≤ 2, y+ 1 ≥a, x, y ≥ 0. (a) Plot the constraints and shade the feasible region. In your plot, label each line which forms the boundary of the feasible region. (b) Write the feasible region in matrix-vector form Ax ≤ b, x ≥ 0. (c) Find all vertices of the feasible region.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.2: Systems Of Linear Equations In Two Variables
Problem 41E
Related questions
Question
![Algebra
Consider the constraints
2x + y ≤ 6,
y-x ≤ 2,
y + 12x,
x, y ≥ 0.
(a) Plot the constraints and shade the feasible region. In your plot,
label each line which forms the boundary of the feasible region.
(b) Write the feasible region in matrix-vector form Ax ≤ b, x > 0.
(c) Find all vertices of the feasible region.
Calculus
In this question, we will use the definition of the integral to evaluate
L₁₁-
1-r² dr.
If we partition the interval [-1,1] into n subintervals, it is difficult
to determine precise expressions for the lower and upper sums due
to the fact that f(x) = 1 - ² is increasing on the interval [-1,0],
and decreasing on the interval [0, 1]. In particular, the expressions
will change depending on whether we take an even or odd number of
subintervals.
One way of dealing with this is to instead compute the integral
[₁1-2² dz,
and exploit the symmetry of the given function f.
(a) Using appropriate summation formulas from lectures, determine
the expressions for Ln and Un. Then find the limit values of Ln
and Un, and hence determine
1
ef₁
1-x² dx.
(b) Using your answer in part (a) and the fact that f is an even
function (i.e. for any x, f(x) = f(-x)), determine [₁1-2² dr.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1034cea3-472e-48dd-9355-35c8e115faad%2Fbb28f073-40e1-4214-bd5d-84d13e4f2fe3%2Fnoumsx_processed.png&w=3840&q=75)
Transcribed Image Text:Algebra
Consider the constraints
2x + y ≤ 6,
y-x ≤ 2,
y + 12x,
x, y ≥ 0.
(a) Plot the constraints and shade the feasible region. In your plot,
label each line which forms the boundary of the feasible region.
(b) Write the feasible region in matrix-vector form Ax ≤ b, x > 0.
(c) Find all vertices of the feasible region.
Calculus
In this question, we will use the definition of the integral to evaluate
L₁₁-
1-r² dr.
If we partition the interval [-1,1] into n subintervals, it is difficult
to determine precise expressions for the lower and upper sums due
to the fact that f(x) = 1 - ² is increasing on the interval [-1,0],
and decreasing on the interval [0, 1]. In particular, the expressions
will change depending on whether we take an even or odd number of
subintervals.
One way of dealing with this is to instead compute the integral
[₁1-2² dz,
and exploit the symmetry of the given function f.
(a) Using appropriate summation formulas from lectures, determine
the expressions for Ln and Un. Then find the limit values of Ln
and Un, and hence determine
1
ef₁
1-x² dx.
(b) Using your answer in part (a) and the fact that f is an even
function (i.e. for any x, f(x) = f(-x)), determine [₁1-2² dr.
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