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MATH 121 DISCUSSION WEEK 5 WORKSHEET
1) Consider the below matrix.
A
=
1
3
5
0
1
5
2
4
1
(a) Find
A

1
.
(b) How do we know that we found the correct
A

1
in part (a)?
(c) Using
A

1
, solve the following system of equations:
x
+
3
y
+
5
z
=

7
y
+
5
z
=
2
2
x
+
4
y
+
z
=
3
2) Consider the below system of inequalities:
8
x
+ 3
y
≥
24
2
x
+ 3
y
≤
12
y
≥
1
(a) How many boundary points and boundary lines does the feasible region of this system have?
(b) Determine if the point (
5
2
,
10
3
) is in the feasible region.
(c) Minimize the objective function 7
x
+ 3
y
subject to the constraints given in the system of
inequalities. At what exact point is this objective function minimized?
(d) Maximize the objective function 5
x
+ 9
y
subject to the constraints given in the system of
inequalities. At what exact point is this objective function maximized?
3)
A wine estate produces white wine and red wine. One bottle of white wine requires $20.00 of
capital costs and 6 hours of labor to produce. Meanwhile, one bottle of red wine requires $25.00
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This note was uploaded on 12/07/2010 for the course MATH Math 121 taught by Professor Beaulieu during the Fall '10 term at UMass (Amherst).
 Fall '10
 Beaulieu
 Math, Equations, Probability

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