2. You have volunteered to coach a basketball team in a local recreational leagu

Question

2. You have volunteered to coach a basketball team in a local recreational league. Eight players (four boys, four girls) have signed up for your squad. After running through a few practices with them, you now have the task of generating a starting lineup for this weekend’s first league game. Assume the following represent the five positions in a basketball starting lineup (center, forward #1, forward #2, guard #1 and guard #2). You recognize that your players have different abilities for each of these positions, and have determined “values” for each combination of player and position. These value estimates are on a scale of 1-10, with the higher values representing a better player for that position. League rules stipulate that at least 2 players of each gender must be in the starting lineup (Jennifer, Amy, Francine and Chelsey are the four girls on your team; the other players are boys). Using the data in GS 4.xlsx, formulate an LP model to determine a starting lineup that maximizes your team’s “value”.

B21. A B C D E F H I J K L M N o P Q R s T 1 Problem 2 3 Value" of assigning basketball players to starting lineup Center Forward Forward 2 Guard Guard 2 5 Jennifer 7.5 8.0 5.5 5.0 6.0 6 Jared 2.0 2.5 4.0 7.5 4.0 6.5 7 Amy 6.0 4.5 5.0 8 Hayd 3.5 5.0 4.0 6.5 5.5 9 Francine 7.0 5.5 5.5 4.5 4.0 10 Mark 5.0 4.5 4.5 9.0 11 Chelsey 2.5 3.0 5.0 12 David 7.0 6.5 6.5 3.0 3.0 15 Assignments 16 Center Forward 1 onward 2 Guard 1 Guard 2 Total 17 Jennifer 18 Jared 19 Army. 20 Hayden Francine 22 Mark 23 Chelsey 24 David 26 Total 27 Required 30 Gender balance Total Minimum 32 Boys 33 Girls 35 Total value Prob 1 Prob 2 Sheet2 Sheet3 Sheet 4 Sheet5 Sheet6 Sheet7 Sheets sheetg 3:37 PM a Ask me anything 3/10/2017

Explanation / Answer

Center Forward 1 Forward 2 Guard 1 Guard 2 Jennifer 7.5 8 5.5 5 6 Jared 2 2.5 4 7.5 4 Amy 6 6.5 7 4.5 5 Hayden 3.5 5 4 6.5 5.5 Francine 7 5.5 5.5 4.5 4 Mark 5 4.5 4.5 9 7 Chelsey 3 4 2.5 7 5 David 7 6.5 6.5 3 3 Center Forward 1 Forward 2 Guard 1 Guard 2 Total SUM Product Jennifer 1 0 0 0 0 1 7.5 Jared 0 0 1 0 0 1 4 Amy 0 1 0 0 0 1 6.5 Hayden 0 0 0 0 0 0 0 Francine 0 0 0 0 0 0 0 Mark 0 0 0 1 0 1 9 Chelsey 0 0 0 0 0 0 0 David 0 0 0 0 1 1 3 Total 1 1 1 1 1 Objective function 30 Constraints Jennifer 1

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