MATH 210
Exam 2
March 19, 1997
For the next two problems, consider the following
1.
Find:
(a)
(b)
(c)
(d)
(e)
None of the above.
2.
Find:
(a)
(b)
(c)
(d)
(e)
None of the above.
3.
A restaurant offers 3 appetizers, 7 entrées, and 2 desserts. How many meals consisting of an appetizer, an entrée and a dessert can be selected?(a)
42
(b)
12
(c)
C(3,7)/2
(d)
(e)
None of the above.
For the next two problems, consider the following:
A pharmaceutical company is investigating the effectiveness of three new tests for a certain disease.
All three tests were given to each of 300 people with the disease.
147 reacted to Test 1. 128 reacted to Test 2. 182 reacted to Test 3.
69 reacted to Test 1 and Test 2. 89 reacted to Test 1 and Test 3. 75 reacted to Test 2 and Test 3.
54 reacted to all three tests.
4.
How many reacted to at least one of the tests?(a)
300
(b)
153
(c)
278
(d)
457
(e)
None of the above.
5.
How many reacted to Test 3 but not to any other test?(a)
182
(b)
113
(c)
72
(d)
43
(e)
None of the above.
6.
How many teams of 3 can an employer choose from a pool of 40 job applicants?(a)
120
(b)
64,000
(c)
9,880
(d)
59,280
(e)
None of the above.
7.
In how many ways can an employer choose 3 people to do 3 different jobs from a pool of 40?(a)
120
(b)
64,000
(c)
9,880
(d)
59,280
(e)
None of the above.
For the next two problems, consider the following:
A basket contains 6 peaches, of which 2 are rotten and 4 are good.
A sample of 3 peaches will be selected.
8.
How many samples of 3 peaches contain at least 1 rotten peach?(a)
20
(b)
4
(c)
16
(d)
7
(e)
None of the above.
9.
How many samples of 3 peaches contain exactly 2 rotten peaches?(a)
20
(b)
4
(c)
1
(d)
6
(e)
None of the above.
10.
A restaurant offers 8 different toppings for pizza.How many different pizzas can be ordered?
(From 0 to 8 toppings may be selected.)
(a)
(b)
8
(c)
8!
(d)
C(8,8)
(e)
None of the above.
For the next two problems, solve the following linear programming problem.
Minimize the objective function:
subject to the constraints:
11.
The minimum value is:(a)
160
(b)
70
(c)
20
(d)
0
(e)
None of the above.
12.
The minimum value occurs at:(a)
( 0, 40 )
(b)
( 30, 70 )
(c)
( 80, 20 )
(d)
( 100, 0 )
(e)
None of the above.
13.
In how many ways can 8 different toys be divided among 4 children, if each child will receive 2 toys?(a)
80,640
(b)
2,520
(c)
105
(d)
40,320
(e)
None of the above.
For the next two questions, set up, BUT DO NOT SOLVE, the following linear programming problem. A dietician is planning a meal consisting of two foods. One ounce of Food I contains 5 units of protein, and 2 units of carbohydrates. One ounce of Food II contains 10 units of protein,
and 3 units of carbohydrates. An ounce of Food I contains 10 calories. An ounce of Food II contains 15 calories. The meal should contain at least 20 units of protein, and at least 10 units of carbohydrates. How many ounces of each food should the meal contain to meet the nutritional requirements with the smallest possible number of calories?
Let x be the number of ounces of Food I in the meal, let y be the number of ounces of Food II in the meal, and let C be the number of calories in the meal.
14.
Express C in terms of x and y.(a)
C = 5x + 10y
(b)
C = 15x + 10y
(c)
C = 2x + 3y
(d)
C = x + y
(e)
None of the above.
15.
The feasible set for this problem is given by:(a)
(b)
(c)
(d)
(e)
None of the above.
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 8/2/97 by Dr. Anders Linnér (alinner@math.niu.edu)