1. Henri Roulant (of "Roulant's Band") recently broke into acting. Henri realizes that the numberof tickets that will be bought for opening night of the his movie premiere is a function of theamount money spent on advertising the week leading up to the movie. Let T(d) be the numberof tickets that will be bought for opening night if d dollars are spent on advertising that week.Henri models T(d) using the formulaT(d) = 20 log(d+ 20) + 400.For any equations that need to be solved in this problem, make sure that you solve themalgebraically by hand, showing each step in the process. Give you answers both in exact formand rounded in a way that makes sense in the context of the problem.a) How many tickets does Henri expect will be bought if no money is spent on advertisingduring that week?b) How many tickets does Henri expect will be bought if $18, 880 are spent on advertisingduring that week?c) The movie is a success if 600 tickets are sold. How much money does Henri's model indicateshould be spent on advertising that week for the movie to be considered successful?d) Henri realizes that on opening night "Roulant's Band" is also scheduled to perform aconcert. The number of concert tickets sold to see the band is given by the functionC(d) = 40 log((d + 20)²) + 100,where d is the number of dollars that the band spends on advertising the concert duringthe week leading up to the concert. If both the band and the movie company hope tospend the same amount of advertising money and sell the same number of tickets, howmuch should they spend during the week? Will Henri's movie be a success?

Let Td be the number of tickets that will be bought for opening night if d dollars are spent on advertising that week. Henri models Td using the formula, Td=20logd+20+400If no money is spent on advertising, then d=0 T0=20log0+20+400 =20log20+400 =426.0206 ≈426 number of tickets cannot be fractional Henri expects approximately 426 tickets will be bought if no money is spent on advertising during that week.If $18,880 is spent on advertising, then d=18880 T18880=20log18880+20+400 =20log18900+400 =485.5292 ≈486 number of tickets cannot be fractional Henri expects approximately 486 tickets will be bought if $18,880 are spent on advertising during that week. We need to find d when Td=600 Td=20logd+20+400=600⇒20logd+20=600-400⇒20logd+20=200⇒logd+20=20020⇒logd+20=10⇒d+20=1010⇒d=1010-20⇒d=9,999,999,980 Henri should spend atleast $9,999,999,980 on advertising that week for the movie to be considered successful. Equating the number of tickets we get: Td=Cd20logd+20+400=40logd+202+10020logd+20+400=40·2logd+20+100 using logab=b·loga20logd+20+400=80logd+20+10080logd+20-20logd+20=400-10060logd+20=300logd+20=30060logd+20=5d+20=105d=105-20d=99980 It means they should spend $99980 during the week. For d=99980 T99980=20log99980+20+400=500 The movie is a success if 600 tickets are sold. But for $99980, Henry could only sell 500 tickets. That means the movie will not be a success. Answer(d): They should spend $99980 during the week. Henri's movie will not be a success.