A college intermural four-man basketball team is trying to choose its starting line-up from a six-man roster so as to maximize average height. The roster follows:

The starting line-up must satisfy the following constraints:

i) At least one guard must start.

ii) Either John or Ken must be held in reserve.

iii) Only one center can start.

iv) If John or Rich starts, then Jim cannot start.

Formulate this problem as an integer program.

Solve for the optimal starting line-up, using the implicit enumeration algorithm.

Player Number Height* Position Dave 1 10 Center John 2 9 Center Mark 3 Forward Rich Forward Ken Guard Jim Guard 4 5 6 699 6 4 -1 * In inches over 5' 6".