Test 2, Version A
MA 114-004 Fall 2014
Directions:
• There are six questions, some with multiple parts.
• Show all work. Responses for which it is unclear how the answer was obtained will not
receive credit (even if the final answer is correct).
• No calculators are allowed.
• Circle or otherwise indicate your final answers.
• Good luck!
1. (20 points) Use the Simplex Method to maximize 3x+5y+12z subject to the constraints
8
4x + 6y
7z  16
>
>
>
< 3x + 2y
 11
>
9y + 3z  21
>
>
:
x 0, y 0, z 0
2. The questions refer to the following linear programming problem:
Maximize 10x + 12y + 10z
8
x
2y

>
>
>
< 3x
+ z 
>
y + 3z 
>
>
:
x 0, y 0, z 0
subject to the constraints
6
9
12
(a) (5 points)Write the components A, X, B, and C of the problem in matrix form:
‘Maximize CX subject to AX  B.’ You do not need to solve the problem.
(b) (10 points) Write down the associated dual problem. You do not need to solve the
problem.
3. (25 points) An automobile insurance company classifies applicants by their driving
records for the previous three years. Let
S = {applicants who have received speeding tickets},
A = {applicants who have caused accidents},
D = {applicants who have been arrested for driving while intoxicated (DWI)}.
Describe the following sets using set-theoretic notation:
(a)
(i) {applicants who have not received speeding tickets}
(ii) {applicants who have caused accidents and been arrested for DWI}
(iii) {applicants who have not been arrested for DWI, but have received speeding
tickets or caused accidents}
(iv) {applicants who have not caused accidents or have not been arrested for
DWI}
(b) Use one of DeMorgan’s laws to represent number (iv) of part (a) in a di↵erent but
equivalent way.
4. (a) (10 points) Draw a three-circle Venn diagram with sets R, S, and T , and shade in
the portion corresponding to the set R [ (S \ T ).
(b) (10 points) Describe the shaded portion of the Venn diagram in set-theoretic notation:
S
T
5. (a) (5 points) Write the formula for computing the number of permutations of n objects
taken r at a time.
(b) (5 points) Write the formula for computing the number of combinations of n objects
taken r at a time.
6. A student must choose five courses out of the seven she would like to take. Only one
section of each course is being o↵ered. These are the only courses the student will take
this semester.
(a) (5 points) Is the selection of courses described by combinations or permutations?
(b) (5 points) How many possible schedules could the student have this semester?
Extra Credit: (5 points) Each day, Gloria dresses in a blouse, a skirt, and shoes. She wants
to wear a di↵erent combination on every day of the year. If the has the same number
of blouses, skirts, and pairs of shoes, how many of each article would she need to have a
di↵erent combination each day? Explain your reasoning.