Solve using the graphical method. Choose your variables, write the objective function and the constraints, graph constraints, shade feasibility region, label all corner points, and determine the solution that optimizes the objective function.
1)
The chemistry department a local college decides to stock at least 900 small test tubes and 600 large test tubes. It wants to buy at least 2700 test tubes to take advantage of a special price. Since the small test tubes are broken twice as often as the large, the department will order at least twice as many small test tubes as large.
a) If small test tubes cost 18 cents each and the large ones made of a cheaper glass cost 15 cents each, how many of each size should be ordered to minimize cost?
Use a Venn Diagram and the given information to determine the number of elements in the indicated region.
2)
Let U = {a, l, i, t, e}, A = {l, i, t},B = {l, e}, C = {a, l, i, t, e}, and D = {a, e}. Find (C ∩ B’) ∪ A’.
Use the Venn diagram below to find the number of elements in the region.
3)
n((A ∪ B) ∩ C)
Find the number of the elements in the following sets using a Venn Diagram.
4)
In a group of 42 students, 22 take history, 17 take biology and 8 take both history and biology.
How many students take neither biology nor history?
Do the following problem using the multiplication axiom.
5)
A combination lock on a suitcase has 5 wheels, each labeled with digits 1 to 8. How many 5-digit combination lock codes are possible if no digit can be repeated?
Provide an appropriate response.
6)
At Theresa’s Restaurant, each lunch special consists of a sandwich, a beverage, and a dessert. The sandwich choices are roast beef (r) or ham (h). The beverage choices are coffee (c), tea (t), or soda (s). The desert choices are ice cream (i) or apple pie (p).
a) Use the counting principle to determine the number of different lunch specials.
b) Construct a tree diagram and list the different possibilities.
Evaluate.
7)
Do the following problem using the formula for a permutation.
8)
A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 7 different flags available, how many possible signals can be flown?
Do the following problem using the formula for a combination.
9.) In how many ways can a student select 8 out of 10 questions to work on an exam?
10) Solve the problem using either the formula for a permutation or combination.
In a Power Ball lottery, 5 numbers between 1 and 12 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is not important.
11.) Create a frequency table and histogram using the following scores from a recent high school English test:
81
77
63
92
97
68
72
88
78
96
85
70
66
95
80
99
63
58
83
93
75
89
94
92
85
76
90
87
Interval
Frequency
51 – 60
61 – 70
71 – 80
81 – 90
91 – 100