Problem 4 An amusement park has 5 major attractions: The Cork Screw, The Caramel Carousel, The Cranium, The Wave Swinger, and the Sky Flyer. Listed below are the probabilities at which a person moves between rides. For example, if a person is currently riding the Cork Screw they will ride the Cranium next to . 19 probability. A)The amusement park is expected on average 2,000 customers per day. Assuming each customer rides 10 rides in a given day, what is the volume for each of the rides (how many people will ride each ride? B)If a person rides the Cork Screw, on average how many rides will they ride before they return to ride the Cork Screw again? C)The average waiting times are shown in the following table (assume the waiting times are how long a person stands in line and how long it takes to ride the ride, the waiting time basically is the total time from start to end of the ride). If on average it takes a person 5 minutes to walk between each ride and they have to wait in line according to the waiting times on the table and a person just rode the Cranium, how long (in minutes) will it be before they return to ride the Cranium again?TRANSITION MATRIX 1(corkscrew)2(carousel)3(cranium)4(wave swinger5(sky flyer) 1(corkscrew).
23. 10. 19. 23. 25 2(carousel). 12. 07. 18.
42. 21 3 (cranium). 3. 08. 16.
24. 22 4(wave swinger). 4. 12. 15. 09. 24 5(sky flyer). 09.
09. 28. 11. 43 Average Waiting Times RideWait Time (Min 142 210 325 418 533 Problem 5 Suppose you have the following manufacturing process.
You decide that you are going to acquire enough raw materials to manufacture 1,000 items. Each item will require $20 worth of raw material and the rework costs, scrap costs and benefit are provided along with the transition probabilities in the following diagram.The scrap cost is not the sum of the processing cost and raw material, it is the cost that will be incurred if the item is scrapped. A)What will be your total profit? B)How many items will be accepted as good products? C)) How many items will be refurbished products? Justify your answers using a Markovian approach.
Please provide the A, 0, R, and Q matrices along with the F and M matrices. Also provide your profit equation in terms of the probabilities from your matrices.