Problems:
Complete each problem below. You must show all of your work to receive credit for a problem.
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