OREM $3360($Spring $2024)$

SMU

Problem $4()$

$(20$ pts$.)$

To celebrate the completion of Spring $20224$ final examinations, you and five of your friends have decided to go camping to Big Bend National Park! Typically, camping involves activities such as clearing the camp site, setting$-$up the tent, cooking, cleaning dishes and collecting wood. Each one of you is skilled differently in each of these tasks, and the skill levels $(1-10($best$))$ are given in the table below:

$\backslash$table$[[,,,,$Col,$],[$Friend$*-$Task,Clear$-$site,Setup tent,Cook,Clean dishes,Collect wood$],[$You:$,7,9,7,6,5],[$F$1$:$,8,7,8,6,8],[$F$2$:$,5,9,7,8,8],[$F$3$:$,3,7,4,8,9],[$F$4$:$,7,5,9,6,9],[$F$5$:$,9,8,6,5,6]]$

Write a linear programming model suitable for the above problem. As always, an algebraic form with clear definitions will fetch you full credits.