A young couple, Eve and Steven, want to divide their main household chores (shopping, 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:
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Time Needed per Week (Hours)
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Shopping
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Cooking
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Dish Washing
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Laundry
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Eve
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4.5
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7.8
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3.6
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2.9
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Steven
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4.9
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7.2
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4.3
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3.1
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Formulate a binary integer programming model for this problem and solve the model on a spreadsheet.