Present the algebraic models for the following problems by defining variables and formulating objective functions and constraints.

$10\mathrm{.}3.*$ A young couple, Eve and Steven, want to divide their main household chores $($marketing$,$ cooking, dishwashing, and laundering$)$ between them so that each has two tasks but the total time they spend on household duties is kept to a minimum. Their efficiencies on these tasks differ, where the time each would need to perform the task is given by the following table.

$\backslash$table$[[,$Time Needed per Week $($Hours$)],[,$Marketing,Cooking,Dish Washing,Laundry$],[$Eve$,4\mathrm{.}5,7\mathrm{.}8,3\mathrm{.}6,2\mathrm{.}9],[$Steven$,4\mathrm{.}9,7\mathrm{.}2,4\mathrm{.}3,3\mathrm{.}1]]$

a$.$ Formulate a BIP model in algebraic form for this problem.

b$.$ Formulate and solve this model on a spreadsheet.