QUESTIONS 1) Sinem spends 5 hours a day for social network shares on the internet. If she spends 1 hour on Facebook, she gets new friends, 2 likes, 3 shares; whereas she gets 5 new friends, 5 likes, 2 shares on Twitter for 1hr. Popularity index for 1 new friend is 100,1 like is 50,1 share is 75 both on Facebook and Twitter. She is spending time more than twice on Facebook compared to Twitter. She spends minimum 20 minutes on Twitter daily. Construct the mathematical model which maximizes the daily popularity index of Sinem and determines the optimum Facebook and Twitter usage durations. Describe the decision variables of the model clearly. Write and explain the objective function and constraints of your model. (30p.)