6. (15 pts 1 Coach Ahmet is trying to choose the starting lineup for the basketb

Question

6. (15 pts 1 Coach Ahmet is trying to choose the starting lineup 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 and the players abilities are listed in Table below. The five-player starting lineup must satisty the following restrictions 1. At least 4 members must be able to play guard, at least 2 members must be able to play forward, and at least 1 member must be able to play center 2 The average ball handing, shooting, and rebounding level of the starting lineup must be at least 2 3 4 If player 3 starts, then player 0 cannot start Either player 2 or player 3 must start Given these constraints,Coach Ahmet wants to maximize the total defensive ability of the starting team. Formulate a BIP that will hajp him choose his starting team (Do not aolve) Postion Ball HandnShooting Rebounding Defense Guard C Center orwarg

Explanation / Answer

Answer:-

The above is a Integer lInera Programming Problem , where the objective of the firm is to maximise total defensive ability.

Let x1, x2,x3,x4,x5,x6,x7 are be the players, 1,2,3,4,5,6 and 7 Respectivley..

The objective of the firm is to maximise total Defensive ability

Max Z = 3x1+2x2+2x3+x4+2x5+3x6+x7

Subject to

x1+x3+x5+x7>=3 ( Atleast three members must play guard)

x3+x4+x5+x6+x7>= 2 ( Atleast two members must play forward)

x2+x4+x6>=1 ( Atleast one member must play CENTER)

3x1+2x2+2x3+x4+x5+3x6+3x7>=1.8 ( Average ball handling should be atleast 1.8)

3x1+x2+3x3+3x4+3x5+x6+2x7>=1.8 (Average Shooting should be atleast 1.8)

x1+3x2+2x3+3x4+x5+2x6+2x7>=1.8 (Average Rebounding should be atleast 1.8)

x2+x3>=1 ( Either player 2 or player 3 must start)

x1,x2,x3,x4,x5,x6,x7>=0 (Non negatiivity)

x1,x2,x3,x4,x5,x6,x7 is an integers

The solver solution to the problem is given below

The objective Funtion

Max Z 9

X1 0
X2 0
X3 3
X4 0
X5 0
X6 1
X7 0

Constraints

3 3
4 2
1 1
9 1.8
10 1.8
8 1.8
3 1

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