Integer Programming Question:

Joe Maddon is choosing the starting 4 pitchers for the Cubs World Series rotation. He has 7 possible pitchers to choose from who are rated (on a scale of 1=poor to 5=excellent) according to their curve-ball, sinker, slider, and fast ball, and overall ERA. The type of pitcher (R=righty, L=Lefty, B=both) and the pitchers abilities are below:

Player	Type	Curve	Sinker	Slider	Fast	ERA
1	R	4	1	4	2	1.3
2	L	5	3	4	2	2.0
3	B	2	4	5	3	.69
4	L	3	4	2	4	1.4
5	R	4	2	3	5	1.2
6	R	4	5	3	5	1.0
7	B	1	1	1	2	.98

An integer program can be used to help him choose his starting 4 pitchers so that he maximizes the ERA subject to the following constraints:

At least 2 pitchers must be right-handed, at least 1 pitcher must be left-handed and at least 1 must pitch both ways

The average curve ball rating must be at least 3.2, the average sinker at least 3.6, the average slider 2.9, and the average fast ball 3.0

If player 5 starts, then players 2 and 7 must both start

If player 7 starts, then player 1 cannot start, and vice-versa

Either player 3 or 4 (or both) must start

Note: Please ensure you understand how to do this entire problem, even though I am only asking for a portion of it in this problem. The posted solutions will include the entire answer.

Which of the following represents the constraint that the average curve ball rating must be at least 3.2

Answer Choices:

3.2 (4p1 +52 +2p3 +34 +45 +4p6+7) 4 3.2