MATH 106 QUIZ 4 | Complete Solution

INSTRUCTIONS

•The quiz is worth 100 points. There are 10 problems (each worth 10 points).
•This quiz is open book and open notes, unlimited time. This means that you may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our course schedule of the syllabus.
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MULTIPLE CHOICE.  Choose the one alternative that best completes the statement or answers the question.

1) Find the maximum value of the function, if it exists, on the given feasible region.
        Find the maximum of z =   4x +  8y                1)   _______
A) 102

B) 120

C) 76

D) 112

E) none of the above


2)  Find the minimum value of the function, if it exists, on the given feasible region.        Find the minimum of    z = x -  2y                        2)   _______

A) -1

B) -13

C) -28

D) -16

E)  None of the above

3) Use graphical methods to solve the linear programming problem.
                                            3) _________
Maximize        z = 6x + 7y 
   
Subject to:        2x + 3y ≤ 12
                2x + y ≤ 8
                x ≥ 0
                y ≥ 0

A)    Maximum of 32 when x = 3 and y = 2

B)    Maximum of 32 when x = 2 and y = 3

C)    Maximum of 24 when x = 4 and y = 0

D)    Maximum of 52 when x = 4 and y = 4

E)    None of the above

4)  A college student can spend no more than 8 hours a week tutoring. She charges $10 an hour to tutor finite math and $13 to tutor algebra. She limits herself to no more than 3 hours per week to tutor algebra and spends at least 1 hour a week tutoring each subject. How many hours per week should she spend tutoring each subject to maximize her income? What is her maximum weekly income?
4) _________
Hint:  Let x = number of hours per week to tutor finite math   and
y = number of hours per week to tutor algebra
Then use graphical methods to solve the following linear programming problem:
Maximize        z = 10x + 13y 
                            Subject to:            x + y ≤ 8
                                        y ≤ 3
                                        x ≥ 1
                                        y ≥ 1

A)    4 hours of finite math and 4 hours of algebra; maximum income is $92 per week

B)    7 hours of finite math and 1 hour of algebra; maximum income is $83 per week

C)    5 hours of finite math and 3 hours of algebra; maximum income is $89 per week

D)    3 hours of finite math and 5 hours of algebra; maximum income is $95 per week

E)    None of the above


5) Let U = {q, r, s, t, u, v, w, x, y, z},    A = {q, s, u, w, y},      B = {q, s, y, z},    and
 C = {v, w, x, y, z}.            
Find the elements in the set A ∩ B'            5)   _______

A) {t, v, x}

B) {u, w}

C) {r, s, t, u, v, w, x, z}

D) {q, s, t, u, v, w, x, y}

E)  None of the above

6)  Use the counting formula to solve the following problem.

If n(B) =  12, n(A ∩ B) =  3, and n(A ∪ B) =  21, find n(A).                6)   _______

A) 12

B) 14

C) 9

D) 10

E)  None of the above

7)  If n(A) =  32, n(B) =  93 and n(A ∪ B) =  109, what is n(A ∩ B)?        7)   _______

A) 8

B) 18

C) 48

D) 16

E)  None of the above

Solve the following problems.

8)  At East Zone University (EZU) there are  897 students taking College Algebra or Calculus.  520 are taking College Algebra,  450 are taking Calculus, and  73 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus?                                                            8)   _______

A) 824

B) 374

C) 377

D) 447

E)  None of the above

9) A restaurant offered salads with  8 types of dressings and  4 different toppings. How many different types of salads could be offered?                        9)   _______

A) 32 types

B) 16 types

C) 12 types

D) 64 types

E)  None of the above

10) How many ways can a committee of  5 be selected from a club with  10 members?
                       
                                            10)   ______
A) 30,240

B) 252

C) 50

D) 100,000

E)  None of the above