Jennifer's Spa offers various health treatments such as facial, massage, power shower, mineral bath, and sauna....

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Jennifer's Spa offers various health treatments such as facial, massage, power shower, mineral bath, and sauna. The spa incurs a setup cost for each of those services, so that Jennifer would like to estimate the expected overall setup cost for a customer going through the spa. The problem is that each customer varies in their selection of services. For instance, a customer may go for a facial and sauna while another customer may only go for a massage. Jennifer has collected data on the customer movement between spa activities, as summarized in the following table: Relaxation Lounge Facial Massage Power Shower Mineral Bath Sauna Facial 75 Massage Power Shower Mineral Bath 50 25 20 90 Saunal 60 50 Leave Spa 40 20 20 60 80 Total 150 100 110 70 80 80 For example, of 100 customers who did a facial, 60 went to the sauna next and 40 left the spa. Customers always enter the spa and stay first at the relaxation lounge before going to any other activity. Notice that starting at the lounge, the longest sequence of steps before leaving the spa is four: lounge -> mineral bath -> massage -> power shower -> sauna. Also notice that customers always leave after the sauna. To help Jennifer, perform the following tasks: 1. Model this problem as a Markov chain by explicitly providing a one-step transition matrix P. In your model, a state represents the current location of customer going through the spa. Hence, your model must have seven states: lounge, facial, massage, power shower, mineral bath, sauna, and leave spa, and matrix P should have dimensions 7 x 7. A step represents a customer moving from one activity to another activity. 2. Write an R function called "spa.cost" that has one parameter named "setup.cost". The "setup.cost" parameter is a vector of dimension 5 containing the setup costs for each of the five treatments (facial, massage, power shower, mineral bath, and sauna), there is no cost for the lounge or for leaving the spa. The function will compute the expected setup cost per customer of going through the spa when starting from the lounge (Hint. Compute the one-step expected setup cost, the two-step expected setup cost, the three-step expected setup cost, and the four-step expected setup cost, then return the sum of the four numbers). 3. Prepare a Shiny app with five sliders, one for each treatment, to input the setup costs of the treatments. Each slider will range from 0 to 100 in increments of 1, default value is 10. The app should call the "spa.cost" function with the corresponding setup costs for the treatments and display the resulting expected setup cost on an output text box. 4. Report your transition matrix P and copy-paste the R code on your Word file. Jennifer's Spa offers various health treatments such as facial, massage, power shower, mineral bath, and sauna. The spa incurs a setup cost for each of those services, so that Jennifer would like to estimate the expected overall setup cost for a customer going through the spa. The problem is that each customer varies in their selection of services. For instance, a customer may go for a facial and sauna while another customer may only go for a massage. Jennifer has collected data on the customer movement between spa activities, as summarized in the following table: Relaxation Lounge Facial Massage Power Shower Mineral Bath Sauna Facial 75 Massage Power Shower Mineral Bath 50 25 20 90 Saunal 60 50 Leave Spa 40 20 20 60 80 Total 150 100 110 70 80 80 For example, of 100 customers who did a facial, 60 went to the sauna next and 40 left the spa. Customers always enter the spa and stay first at the relaxation lounge before going to any other activity. Notice that starting at the lounge, the longest sequence of steps before leaving the spa is four: lounge -> mineral bath -> massage -> power shower -> sauna. Also notice that customers always leave after the sauna. To help Jennifer, perform the following tasks: 1. Model this problem as a Markov chain by explicitly providing a one-step transition matrix P. In your model, a state represents the current location of customer going through the spa. Hence, your model must have seven states: lounge, facial, massage, power shower, mineral bath, sauna, and leave spa, and matrix P should have dimensions 7 x 7. A step represents a customer moving from one activity to another activity. 2. Write an R function called "spa.cost" that has one parameter named "setup.cost". The "setup.cost" parameter is a vector of dimension 5 containing the setup costs for each of the five treatments (facial, massage, power shower, mineral bath, and sauna), there is no cost for the lounge or for leaving the spa. The function will compute the expected setup cost per customer of going through the spa when starting from the lounge (Hint. Compute the one-step expected setup cost, the two-step expected setup cost, the three-step expected setup cost, and the four-step expected setup cost, then return the sum of the four numbers). 3. Prepare a Shiny app with five sliders, one for each treatment, to input the setup costs of the treatments. Each slider will range from 0 to 100 in increments of 1, default value is 10. The app should call the "spa.cost" function with the corresponding setup costs for the treatments and display the resulting expected setup cost on an output text box. 4. Report your transition matrix P and copy-paste the R code on your Word file.