Mathematics

Hints and Answers

Section 3.2

13. After one or two steps of the simplex method (depending on how you do it), all the rows end with a positive number, but there is still a column whose bottom entry is negative. So we go back to our original simplex method. Unfortunately, all the entries in that column are negative, so we cannot find a pivot.

Section 5.4

8. (a) 3/10 (b) 9/10 (c) 1/3 (d) 1/2
12. (a) 1/625 (b) 1/125 (c) 1/120 (d) 12/125
14. (a) 1/5 (b) 2/9 (c) 1/9

Section 5.5

4. (b) .784 (c) .64
6. 8/13
12. (a) 1/5 (b) 3/5

Section 5.7

13. (a) To get the book's answer, think of the "amount of money that Paul will receive" as 5 dollars if he wins AND -5 DOLLARS IF HE LOSES. Parts b and c are similar.

Chapter 5 Review Problems

11. To get the book's answer, think of the problem like this: Kay's goal is to FIND, not open, the two pieces of candy that she likes. Once she has opened four pieces of candy, even if three of them are ones she dislikes, she has "found" the two she likes: one is the unopened piece. Thus Kay never opens more than four pieces of candy.

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