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MAT 118 Chapter 7 Performance Assessment: You are not allowed to receive any
outside help on this exam. Do not ask other students, faculty, the math clinic, a
tutor, etc. for any help. If you have a question, you can only ask your instructor.
You can use your textbook, notes, calculator, etc.)
(Total possible points =15)
This semester we have discussed various approaches to solving linear programming problems. To solve linear programming problems with 3 or more variables we used the simplex
method, however, it is still possible to use the graphical method to solve a linear programming problem that has 3 variables. In this performance assessment we will explore such a
problem both graphically and with the simplex method.
1. Use the following table to determine the two numbers a and b that you will be using
throughout this assessment.
(a) Write your name as it appears on Banner:
Name:
First name starts with:
a=
Last name starts with:
b=
A–F
2
A–F
6
G–L
3
G–L
7
M–Q
4
M–Q
8
R–Z
5
R–Z
9
(b) Using the table above, fill in your values for a and b and let c = a · b:
a=
b=
c=
2. Consider the following linear programming problem:
maximize
subject to
w = −x − 2y + 10z
bx + ay + cz ≤ c
x ≥ 0, y ≥ 0, z ≥ 0
Plug your values in for a, b and c into the linear programming problem above and fill
in your results below. This is the linear programming problem you will solve in this
performance assessment.
maximize
subject to
x+
w = −x − 2y + 10z
y+
z≤
x ≥ 0, y ≥ 0, z ≥ 0
3. (6 points) The graphical method still applies to this linear programming problem. A
sketch of the feasible region, including the corner points of the region is provided below.
Find the solution to the linear programming problem using the graphical method. Show
all of your work in the space provided below the figure.
(0, 0, 1)
z
(0, 0, 0)
(0, b, 0) y
(a, 0, 0)
x
4. (5 points) This problem can also be solved using the simplex method. Using your
values for a, b and c in part 2 write down the initial tableau for your linear programming
problem in the space provided below. Circle the pivot column and row.
x
y
z
s1
w
1
5. (1 point) Is s1 in the tableau in part 4 a slack variable or a surplus variable?
6. (2 points) By following the prompts at http://simplex.tode.cz/en/ use the simplex
calculator at this link to solve your linear programming problem. After entering the
linear programming problem and clicking solve, click on ’Generate Link’ at the bottom
of the page. Include this link with your performance assessment submission.
7. (1 point) Compare your answer in part 6 to your answer in part 3. Are they the same?
If they are not the same, is that reasonable?
2
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