1. Linear programming problem.
Maximize function: P=10x+5y
subject to the following constrains:
3x+6y≤18
2x–y≤2
x ≥0,
y ≥0
Steps to follow:
· Graph all border lines.
· Shade the area where all constrains are satisfied.
· Identify coordinates of corner points.
· Calculate P function at every corner point.
· Identify point where P function has maximum value.
2. For the two given sets S1: {1, 5, 6, 10} and S2: {5, 6, 10, 12}
write the resulting set:
(a) S1 ⋃ S2
(b) S1 ⋂ S2
3. On the given Venn diagram
30 is the total number of elements in the whole array,
10 is the number of elements in the full blue circle (subset A),
15 is the number of elements in the full yellow circle (subset B),
5 is the number of elements that belong to both subsets A and B.
How many elements are in the set:
(a) A ⋃ B
30
15
10
5
(b) (A⋂B)’ meaning, not in (A⋂B).
4. Fast food restaurant has on the menu 3 soups, 5 sandwiches and 6 soft drinks.
In how many different ways can you order one soup, one sandwich and one drink?
5. How many passwords can be created with two letters followed with two numerical digits
(like AD18, DM49 and so on). Second letter should be different from first letter,
and second digit number should be different from first number (like BB23 or AF55 are not accepted). Use counting rule to calculate the total number of possible passwords.
Remember, there are 26 letters in alphabet and 10 possible numerical digits.
6. Use definition of factorial (!) to simplify and calculate 8!/6! without using a calculator.
7. There are 5 teams in a group. In how many ways can be one team on the first place, another team on the second and other team on the third?
Order of teams matters (what team on the first place, what team on the second and third).
So, use formula for Permutation.
8. In how many ways can you select 4 different shirts out of 10 to take with you on a trip? Order of selection doesn’t matter – use formula for Combination.
9. A committee of four is selected from a total of 4 freshmen, 5 sophomores, and 6 juniors. Find the probabilities for the following events.
a. at least three freshmen
b. all four of the same clas
c. not all four from the same class
d. exactly three of the same class
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