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The Toronto Raptors are planning for the years ahead and the team’s General Manager has six

The Toronto Raptors are planning for the years ahead and the team’s General Manager has six player contracts that he must consider for renewal this summer. However, due to salary cap regulations, he cannot resign all six players. The following table displays the player ratings based on advanced metrics and the required yearly salary to be paid to each player.

   

Salary (in $millions) required per year

Player

Player Rating

Year 1

Year 2

Year 3

Year 4

Year 5

1

2

3

4

5

6

65

83

70

75

88

69

$6.3

$12.0

$2.0

$5.8

$18.5

$2.1

$3.5

$8.0

$2.5

$9.8

$18.9

$2.4

$2.0

$8.0

$3.8

$12.1

$19.3

$0

$1.2

$0

$5.9

$14.2

$21.8

$0

$0.8

$0

$8.0

$18.6

$0

$0

The total salary budget available and allocated for these players for each year is shown in the following table:

Salary cap (in $millions) allocated per year

Year 1

Year 2

Year 3

Year 4

Year 5

$30

$33

$31

$26

$28

In addition, the team must follow a few league regulations for signing players based on their contract types:

  1. Money left over in any year cannot be carried over from year to year.

  2. If the team decides to sign player 2 to a contract, it must also sign player 4.

  3. If the team decides to sign player 1 to a contract, it cannot sign player 3 to a contract.

Considering the budget limitation and the league regulations, which players should the General Manager sign to a contract this summer in order to maximize the player ratings for the team? Formulate the linear programming model in algebraic form, and solve it using Excel Solver. Provide the layout of your Excel and answer report. Solve this problem using only the information given in the problem and ignore the league’s actual collective bargaining agreement.

Feb 06 2020 View more View Less

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