Melissa Beadle is a student at Tech, and she wants to decide how many hours each day to allocate to the following activities: class; studying; leisure and fun stuff; personal activities such as eating, bathing, cleaning, laundry, and so on; and sleeping. She has established weights indicating how her different activity hours relate to raising her grade point average. Each hour she spends in class will raise her GPA by 0.3 points, 1 hour of studying will raise her GPA by 0.2 points, leisure and fun activities will raise her GPA by 0.05 points per hour, personal activities will raise her GPA by 0.10 points per hour, and sleep will increase her GPA by 0.15 points per hour. Melissa has only 4 hours of class each day, and she knows she won't study more than 8 hours in a day. She thinks she could spend up to 10 hours a day on leisure and having fun, she'll spend at least 2 hours but not more than 3 hours on personal stuff, and she'll sleep at least 3 hours per day but not more than 10 hours.
a. Formulate a linear programming model that will allocate Melissa's hours each day so that her GPA (on a 4.0 scale) will be maximized. Reformulate the model to reflect your own personal preferences relative to your daily activities.