exam

MATH 210

Exam 2

October 23, 1996

For the next two problems, consider the following:

U={1,2,3,4,5,6,7,8,9,10}

A={1,3,5,9}

B={1,2,3,4}

1. Find

(a)

{1,2,3,4,5,9}

(b)

{1,3}

(c)

{2,4,5,9}

(d)

{2,4}

(e)

None of the above.

2. Find

(a)

{1,2,3,4,5,9}

(b)

{1,3}

(c)

{5,9}

(d)

{2,4}

(e)

None of the above.

3. For sets A and B, which of the following are ALWAYS true?

(a)

(i) only.

(b)

(ii) only.

(c)

(i) and (iv) only.

(d)

(ii), (iii) and (iv) only.

(e)

Some other selection.

For the next two problems, consider the following:

A survey of 500 students yielded the following information:

180 take Math.

200 take Spanish.

192 take English.

84 take Math and Spanish.

52 take Math and English.

64 take Spanish and English.

38 take all three subjects.

4. How many take at least one of these subjects?

(a)

500

(b)

286

(c)

124

(d)

410

(e)

None of the above.

5. How many take exactly one of these subjects?

(a)

500

(b)

286

(c)

124

(d)

410

(e)

None of the above.

6. In how many ways can an investor choose 4 mutual funds for her investment portfolio from a recommended list of 8 mutual funds?

(a)

(b)

256

(c)

1680

(d)

(e)

None of the above.

7. A car dealer offers 10 different options (such as air conditioning, sunroof, etc.) on a certain type of car. How many different cars can be bought? (From 0 to 10 options may be selected.)

(a)

(b)

(c)

10!

(d)

(e)

For the next two problems, consider the following:

A box contains 10 balls, of which 2 are red and 8 are green. A sample of 4 balls will be selected.

8. How many samples of 4 balls contain exactly 1 red ball?

(a)

210

(b)

140

(c)

(d)

112

(e)

None of the above.

9. How many samples of 4 balls contain at least 1 red ball?

(a)

210

(b)

140

(c)

(d)

112

(e)

None of the above.

10. In how many ways can 4 couples be seated in a row of 8 seats, if the 4 men must sit together and the 4 women must sit together ?

(a)

40320

(b)

1152

(c)

(d)

65536

(e)

None of the above.

For the next two problems, solve the following linear programming problem.

Minimize the objective function C = x + y subject to the constraints

11. The minimum value is:

(a)

(b)

(c)

(d)

(e)

None of the above.

12. The minimum value occurs at:

(a)

( 6 , 0 )

(b)

( 0 , 14 )

(c)

( 3 , 12 )

(d)

( 21 , 0 )

(e)

None of the above.

13. A group of 9 children is to be divided into 3 teams of 3 to work on identical class projects. In how many ways can this be done?

(a)

(b)

592,704

(c)

280

(d)

1680

(e)

None of the above.

The next two problems refer to the following situation.

A company manufactures two products, A and B, on two machines I and II. The company makes a profit of $3 on each unit of product A and a profit of $4 on each unit of product B. To manufacture a unit of product A requires 6 minutes on machine I and 5 minutes on machine II. To manufacture a unit of product B requires 9 minutes on machine I and 4 minutes on machine II. There are 300 minutes available on machine I and 180 minutes available on machine II.

Let x be the number of units of product A made, and let y be the number of units of product B made.

14. Express the profit P in terms of x and y.

(a)

P = 6x + 9y

(b)

P = 5x + 4y

(c)

P = 3x + 4y

(d)

P = 4x + 3y

(e)

None of the above.