Elphаbа, аn aspiring fitness influencer, is trying tо decide which wоrkоuts she should live stream on TikTok in the upcoming week. She is trying to balance between several alternatives, and factors that are important to her include “Intensity level”, “Morning workout?”, “Impressive for TikTok?”, and “Minutes per Livestream.” The workouts are rated as follows: Workout Running Yoga Strength Training HIIT Pilates Cycling Dance Intensity Level (1 = low, 4 = high) 4 1 3 5 2 4 3 Morning Workout? (1 = Yes, 0 = No) 1 1 0 0 0 0 0 Impressive for TikTok? (1 = low, 4 = high) 3 4 5 2 2 1 5 Minutes per Livestream 90 40 50 50 40 60 40 Elphaba wants to maximize how impressive her live streams are (i.e., maximize the “Impressive for TikTok” score), while satisfying the following requirements: She can include only one workout that is scheduled for the morning She must complete at least 4 different workouts during the week. The average "Intensity Level" of her selected workouts must be at least 3. Elphaba wants to set a limit on her total streaming time. The limit depends on whether or not she includes running, which is time-intensive. She will set either 280 minutes as her limit if she includes running, or 240 minutes if she does not include running. Let Xi = 1 if exercise i is chosen and 0 if not; i = 1 (Running), 2 (Yoga), 3 (Strength Training), 4 (HIIT), 5 (Pilates), 6 (Cycling), 7 (Dance). The binary decision variable implies that Elphaba will stream each chosen workout only once during the week. Which four LINEAR constraints describe the four requirements above? Please check all four constraints.
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