Here’s an assortment of problems from the sections that will be covered on the final exam.

You can use these problems to make a practice test. Make sure you also review test problems from the previous exams for material not included in the book chapters (like the Simplex method and Pascal’s triangle).

**Chapter 1**

- Section 1.2: 15, 17, 19, 39, 41, 43
- Section 1.3: 1,3,5, 9, 11

**Chapter 2**

- Section 2.1: 39, 41, 43, 49, 51
- Section 2.2: 17, 19, 21, 25, 27, 29, 37, 39
- Section 2.3: 33-49 (odds)
- Section 2.4: 1, 19, 21, 25
- Section 2.5: 1-9 (odds)

**Chapter 3**

- Section 3.1: 7, 10, 11, 13
- Section 3.2: 25-31 (odds), 33-41 (odds)
- Section 3.3: 22 (solution: operate refinery I for 4 days and refinery II for 3 days), 23 (see example 1 for a similar problem), 24, 25, 26 (solution: ship 4 cars from Baltimore to Philadelphia, 1 car from Baltimore to Trenton, and 6 cars from NY to Trenton), 31
- Make sure to review the Simplex method as it was presented in class
- Make sure to review finding vertices of higher dimensional feasible sets

**Chapter 5**

- Section 5.1:
** **1-13 odds only, 21-26, and 41-47 (do both even and odds for the last ten problems)
- Section 5.2:
** **15-38 odds only (here are examples where you are shading in a region on a Venn Diagram)
- Section 5.3:
** **11-19 (odds only), 26-30, 61-68 (these last four questions are similar to the flag example we did in class)
- Solutions for Section 5.3:
- solution to problem 26: 102,
- solution to problem 28: 52
- solution to problem 30: 68
- solution to problem 62: 36
- solution to problem 64: 56
- solution to problem 68: 40

- Section 5.4: 1-21 odds only, 37, 38 (The solution for number 38 is 2^5), 49
- Section 5.5: 21-29 odds, 29, 31, 34 (solution: 35*34*33*32*31),35, 37, 39, 49, 51, 61, 63
- Section 5.6: 1,3, 7, 9, 11, 13, 21
- Be sure to review Pascal’s Identity and Pascal’s Triangle!

**Chapter 6**

- Section 6.1: 1, 3, 11, 13, 15, 17, 19, 23
- Section 6.2: 11, 13, 19, 23, 25, 29, 31, 33, 35
- Section 6.3:
** **7, 9,11, 17 (Outcomes are recorded as sequence (a,b,c), in which a, b, and c are days of the week), 21, 25, 27, 29, 33
- Section 6.4: 1, 3, 5, 7, 9, 11, 13, 25, 33, 35, 37, 39, 43, 45, Challenge: 63
- Section 6.5: 1, 3, 5, 7, 9, 11, 13, 17, 25

**Chapter 8**

- Section 8.1: 7-17 (odds only), 19, 21, 23, 25
- Section 8.2:
** **7-15 odds only