(a) Consider the feasible region in R² shown below (the red shaded region). 10 x+y=8 x+y=2 -3x - y = -2 2- =4 I /2 4 8 10 12 14 -2 (i) Express the region using set notation. (ii) Find the vertices. (b) Write the feasible region CCR³, where C = {(x, y, z) | x, y, z ≥ 0, x+z< 1, z−2x ≤ 10, x+y=2z > 1}, in matrix-vector form Ax ≤ b. 00 6

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Consider the feasible region in R² shown below (the red shaded
region).
10
x+y=8
x+y=2
-3x - y = -2
2- =4
I
/2
4
8
10 12 14
-2
(i) Express the region using set notation.
(ii) Find the vertices.
(b) Write the feasible region CCR³, where
C = {(x, y, z) | x, y, z ≥ 0, x+z< 1, z−2x ≤ 10, x+y=2z > 1},
in matrix-vector form
Ax ≤ b.
00
6
Transcribed Image Text:(a) Consider the feasible region in R² shown below (the red shaded region). 10 x+y=8 x+y=2 -3x - y = -2 2- =4 I /2 4 8 10 12 14 -2 (i) Express the region using set notation. (ii) Find the vertices. (b) Write the feasible region CCR³, where C = {(x, y, z) | x, y, z ≥ 0, x+z< 1, z−2x ≤ 10, x+y=2z > 1}, in matrix-vector form Ax ≤ b. 00 6
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