Chapter 4.4, Problem 37E

Study Techniques Your mathematics test is tomorrow and will cover the following topics: game theory, linear programming, and matrix algebra. You have decided to do an all-nighter and must determine how to allocate your 8 hours of study time among the three topics. If you were to spend the entire 8 hours on any one of these topics (thus using a pure strategy), you feel confident that you would earn a 90% score on that portion of the test but would not do so well on the other topics. You have come up with the following table, where the entries are your expected scores. (The fact that linear programming and matrix algebra are used in game theory is reflected in these numbers.)

Test

Your Strategies	Game	Linear Programming	Matrix Algebra
Game Theory	90	70	70
Linear Programming	40	90	40
Matrix Algebra	60	40	90

You have been told that the test will be weighted as follows: game theory: 25%, linear programming: 50%, and matrix algebra: 25%.

a. If you spend 25% of the night on game theory, 50% on linear programming, and 25% on matrix algebra, what score do you expect to get on the test?

b. Is it possible to improve on this by altering your study schedule? If so, what is the highest score you can expect on the test?

c. If your study schedule is according to part (a) and your teacher decides to forget her promises about how the test will be weighted and instead bases it all on a single topic, which topic would be worst for you, and what score could you expect on the test?