A coach is trying to choose the starting line-up for the basketball team. The team consists of seven players who have been rated (on a scale of 1= poor to 3 = excellent) according to their ball-handling, shooting, rebounding, and defensive abilities. The positions that each player is allowed to play (G = guard, C = center, F = forward) and the player’s abilities are: Player Position Defense Ability 1 G 3 2 C 2 3 G-F 2 4 F-C 1 5 G-F 1 6 F-C 3 7 G-F 3 Formulate an IP to choose the starting lineup such that the five-player starting line-up satisfies the following restrictions, then solve your IP using python (if you have not taken and are not currently taking python you may use the excel solver - be sure to document this in your homework submission). Submit your python file on canvas and include the optimal solution in your written submission. (a) At least 3 starters must be able to play guard, at least 2 starters must be able to play forward, and at least one starter must be able to play center. (b) The average defensive ability of the starting lineup must be at least 2. (c) If player 3 starts, then player 6 cannot start. (d) If player 1 starts, then players 4 and 5 must both start. (e) Either player 2 or player 3 (or both) must start.
A coach is trying to choose the starting line-up for the basketball team. The team consists of
seven players who have been rated (on a scale of 1= poor to 3 = excellent) according to their
ball-handling, shooting, rebounding, and defensive abilities. The positions that each player
is allowed to play (G = guard, C = center, F = forward) and the player’s abilities are:
Player Position Defense Ability
1 G 3
2 C 2
3 G-F 2
4 F-C 1
5 G-F 1
6 F-C 3
7 G-F 3
Formulate an IP to choose the starting lineup such that the five-player starting line-up satisfies
the following restrictions, then solve your IP using python (if you have not taken and are not
currently taking python you may use the excel solver - be sure to document this in your
homework submission). Submit your python file on canvas and include the optimal solution
in your written submission.
(a) At least 3 starters must be able to play guard, at least 2 starters must be able to play
forward, and at least one starter must be able to play center.
(b) The average defensive ability of the starting lineup must be at least 2.
(c) If player 3 starts, then player 6 cannot start.
(d) If player 1 starts, then players 4 and 5 must both start.
(e) Either player 2 or player 3 (or both) must start.
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