help with quiz 4

MATH 106 QUIZ 4 NAME: _____ _________________

Professor: Dr. Katiraie

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.

You must show your work to receive full credit. If you do not show your work,

you may earn only partial or no credit at the discretion of the professor. Please

type your work in your copy of the quiz, or if you prefer, create a document containing

your work. Scanned work is acceptable also. Be sure to include your name in the

document.

Consult the Additional Information portion of the online Syllabus for options regarding

the submission of your quiz. If you have any questions, please contact me by e-mail ([email protected] ).

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 = 22x + 2y 1) _______

A) 154

B) 120

C) 162

D) 142

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 = 9x - 2y 2) _______

A) 11 B) 7 C) 55 D) 32

E) None of the above

3) Use graphical methods to solve the linear programming problem. 3) _________

Maximize z = 10x + 2y

Subject to: 2x + 3y ≤ 12 2x + y ≤ 8 x ≥ 0 y ≥ 0

A) Maximum of 49 when x = 3 and y = 2

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

C) Maximum of 40 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 $15

an hour to tutor finite math and $12 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 = 15x + 12y 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 $108 per week

B) 7 hours of finite math and 1 hour of algebra; maximum income is $117 per week

C) 5 hours of finite math and 3 hours of algebra; maximum income is $111 per week

D) 9 hours of finite math and 5 hours of algebra; maximum income is $195 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 ∩ C' 5) _______

A) {t, v, x}

B) {u, w}

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

D) {q, s, u}

E) None of the above

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

If n(B) = 24, n(A ∩ B) = 5, and n(A ∪ B) = 28, find n(A). 6) _______

A) 12

B) 14

C) 9

D) 10

E) None of the above

7) If n(A) = 35, n(B) = 90 and n(A ∪ B) = 110, what is n(A ∩ B)? 7) _______

A) 15

B) 18

C) 28

D) 16

E) None of the above

Solve the following problems.

8) At East Zone University (EZU), 980 students are taking College Algebra or Philosophy. 550

are taking Philosophy, 500 are taking College Algebra, and 70 are taking both College Algebra

and Philosophy. How many are taking College Algebra but not Philosophy?

8) _______

A) 824

B) 430

C) 377

D) 447

E) None of the above

9) A restaurant offered salads with 8 types of dressings and 6 different toppings. How many

different types of salads could be offered? 9) _______

A) 32 types

B) 16 types

C) 12 types

D) 48 types

E) None of the above

10) How many ways can a committee of 4 be selected from a club with 13 members?

10) ______

A) 30,240

B) 17,160

C) 715

D) 100,000

E) None of the above