Chapter 4.4, Problem 40E

Textbook Writing You are writing a college-level textbook on finite mathematics and are trying to come up with the best combination of word problems. Over the years, you have accumulated a collection of amusing problems, serious applications, long complicated problems, and generic problems.²⁴ Before your book is published, it must be scrutinized by several reviewers, who, it seems, are never satisfied with the mix you use. You estimate that there are three kinds of reviewers: the “no-nonsense” types, who prefer applications and generic problems; the “dead serious” types, who feel that a college-level text should contain little or no humor and lots of long complicated problems; and the “laid-back” types, who believe that learning best takes place in a light-hearted atmosphere bordering on anarchy. You have drawn up the following chart, where the payoffs represent the reactions of reviewers on a scale of 210 (ballistic) to 110 (ecstatic):

Reviewers
You		No-Nonsense	Dead Serious	Laid-Back
		Amusing	–5	–10	10
		Serious	5	3	0
		Long	–5	5	3
	Generic	5	3	–10

a. Your first draft of the book contained no generic problems and equal numbers of the other categories. If half the reviewers of your book were “dead serious” and the rest were equally divided between the “no-nonsense” and “laid-back” types, what score would you expect?

b. In your second draft of the book, you tried to balance the content by including some generic problems and eliminating several amusing ones. You wound up with a mix of which one eighth were amusing, one quarter were serious, three eighths were long, and a quarter were generic. What kind of reviewer would be least impressed by this mix?

c. What kind of reviewer would be most impressed by the mix in your second draft?