# In the tickets example, identify a fourth feasible alternative

1-1. In the tickets example, identify a fourth feasible alternative.

1-5. In a baseball game, Jim is the pitcher and Joe is the batter. Suppose that Jim can throw either a fast or a curve ball at random. If Joe correctly predicts a curve ball, he can maintain a .500 batting average, else if Jim throws a curve ball and Joe prepares for a fastball, his batting average is kept down to .200. On the other hand, if Joe Â­correctly predicts a fastball, he gets a .300 batting average, else his batting average is only .100.

1. Define the alternatives for this situation.
2. Define the objective function for the problem, and discuss how it differs from the familiar optimization (maximization or minimization) of a criterion.

1-7. A (two-dimensional) pyramid is constructed in four layers: The bottom layer consists of (equally spaced) dots 1, 2, 3, and 4; the next layer includes dots 5, 6, and 7; the following layer has dots 8 and 9; and the top layer has dot 10. You want to invert the pyramid (i.e., bottom layer has one dot and top layer has four) by moving the dots around.

1. Identify two feasible solutions.
2. Determine the smallest number of moves needed to invert the pyramid.

1-8. You have four chains, each consisting of three solid links. You need to make a bracelet by connecting all four chains. It costs 2 cents to break a link and 3 cents to resolder it.

1. Identify two feasible solutions and evaluate them.
2. Determine the cheapest cost for making the bracelet