$6-$ You and your partner are trying to manage four tasks at home, let's call them A$,$ B$,$ C$,$ and D$.$ You come up with the following table showing how long takes for each of you to do any of the tasks $($in hours$).$ In the table you and your partner are denoted by Y and P$.$ Formulate an abstract $($called symbolic$)$ binary integer programming model for this problem $($in a way that tasks are divided fairly, each person doing two tasks, and all the tasks are done$).$

$\backslash$table$[[,$A$,$B$,$C$,$D$],[$Y$,4\mathrm{.}5,7\mathrm{.}8,3\mathrm{.}6,2\mathrm{.}9],[$P$,4\mathrm{.}9,7\mathrm{.}2,4\mathrm{.}3,3\mathrm{.}1]]$