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Linear Programming

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1.)

Without graphing, determine which of the following three points:

P1 = (8,6)
P2 = (2,5)
P3 = (4,1)

are part of the graph of the following system:

y - 10x <= 0
2y - 3x >= 0
y + x <= 15

2.)

Maximize and minimize the quantity z = 15x + 20y subject to the constraints:

x <= 6
y <= 6
3x + 2y >= 6
x >= 0
y >= 0

3.)

Maximize:

z = 4x + y

subject to the constraints:

0 <= x <= 7
0 <= y <= 8
x + y >= 2

4.) Transpose this augmented matrix:

[ 1 8 7 9 ]
[ 0 2 5 1 ]
[ -4 -1 0 17 ]

5.)

Maximize:
P = 300x1 + 200x2 + 450x3

Subject to :
4x1 + 3x2 + 5x3 <= 140
x1 + x2 + x3 = 30

6.)

Minimize
P = 2x1 + x2

subject to:

2x1 + 2x2 >= 8
x1 - x2 >= 2

7.)

Maximize:

P = x1 + 2x2 + x3

Subject to the constraints:

3x1 + x2 + x3 <= 3
x1 - 10x2 - 4x3 <= 20
x1 >= 0
x2 >= 0
x3 >= 0

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