Explain the optimality principle in the context of dynamic programming.
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Explain the optimality principle in the context of dynamic programming.
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- St. Clair's pre-school creates a budget based on 6 classrooms with an average class size of 15 students each. There are no per student variable costs as most costs are spread across all students in a classroom (for example, the teacher). The Head Teacher set the tuition at $590 per month for 8 months. For the first semester (Sep, Oct, Nov, Dec), the school had 14 students per class, but they added 12 new students to the school in for the second semester thanks to a special promotional plan. St. Clair's had budgeted $2000 for marketing, all of which historically was spent prior to the start of the school year, and this year they actually spent $1,300 in June. In November, however, when they decided to run the special promotion of 1 free month of tuition for January enrollment for the 2nd 4 month semester (Jan, Feb, Mar, Apr). In addition, they spent another $1500 for advertising this promotion. What was St. Clair's actual volume in months of student tuition if the free month is…An online coaching program has been developed for patients with borderline hypertension. A total of 100 patients are randomized to receive the coaching, and 100 patients serve as control subjects. The start-up cost of the coaching program is $2,000 for software, hardware, and office supplies. A part-time nurse is hired for the program, with a salary of $15,000 plus 20% fringe benefits. The cost per year per patient for medication is $1000. It has been shown that for the first year after beginning the program, 90% with coaching were not considered hypertensive (normal or borderline blood pressure) and 10% were prescribed medication to control their blood pressure. In the control group (no coaching), 70% were not considered hypertensive after 1 year and 30% were prescribed blood pressure medication. Patients in the coaching group continue to receive coaching even if they are prescribed medication. Assuming that these probabilities are constant for the next 4 years, and assuming a 3%…A college provides free tutoring services for its students 7 days a week, and the daily requirements for tutors are: Day M T W Th F S Su Requirements 5 4 7 3 6 3 4 Find the minimum number of tutors required if each tutor works 4 days a week and has 3 consecutive days off. Give preference to Saturday and Sunday off in case of a tie. (Hint: Look for group of 3 days with the lowest requirements). Specify the work schedule for each tutor. How much slack does your schedule generate for each day?
- Formulate an LP model for the following problems.1. A furniture company makes two products: book shelves selling for ₱5,000 and cabinetsselling for ₱8,000. The direct cost per unit is ₱3,000 and ₱4,000, respectively. Thecompany has no difficulty in selling all the products it can manufacture. The assemblydepartment has 60 hours available per week and the finishing department can handleup to 48 hours of work per week. Manufacturing one book shelf requires 4 hours inassembly and 2 hours in finishing. Each cabinet requires 2 hours in assembly and 4hours in finishing. How can the management allocate the limited man-hour of the twodepartments in a way which will secure the largest possible net return?The University Research Center wants to forecast the number of students who will enroll in the SABH programs (BSAC, BSMA, BSBA, BSTM, BSHM) next semester, in order to determine how many sections to schedule. The registrar has provided the following enrollment data for the past eight semesters: SEMESTER First Semester, SY 2017-2018 Second Semester, SY 2017-2018 Short Term, SY 2017-2018 First Semester, SY 2018-2019 Second Semester, SY 2018-2019 Short Term, SY 2018-2019 First Semester, SY 2019-2020 Second Semester, SY 2019-2020 STUDENTS ENROLLED IN SABH PROGRAMS 400 450 350 420 500 575 490 650 a. Compute a three-semester moving average forecast for school year 2018-2019 onwards. b. Construct a table showing the exponentially smoothed forecast (a = 0.25) for the enrollment data. C. Construct a table showing the adjusted exponentially smoothed forecast using B 0.3 %3D5. Ann Tyler has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after 1 year is primarily dependent on the interest rate during the next year. 51 The rate is currently 7%, and Ann anticipates that it will stay the same or go up or down by at most two points. The various investment alternatives plus their returns ($10,000s), given the interest rate changes, are shown in the following table: Interest Rate Investment 5% 6% 7% 8% 9% Money market fund Stock growth fund 3.1 4 4.3 -3 -2 2.5 4 Bond fund 6. 3 3 Government fund 4 3.6 3.2 3 2.8 Risk fund -4.5 1.2 8.3 14.7 Savings bonds 3 3 3.2 3.4 3.5 Determine the best investment, using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood
- PROBLEM B As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem-solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem-solving should be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs P10,000 and each training program on problem-solving costs P8,000. 1. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem-solving that should be offered in order to minimize total cost. 2. Graph…Answer the following questions: 1. What are the general classifications of Optimization? 2. What is the main objective of a facility location? 3. What type of optimization is facility location? Justify your answer. 4. What are the types of Mathematical Models for Facility Location problems?To what extent may the concept of optimality be used in dynamic programming?
- Describe the optimality principle in terms of dynamic programming.Here is the questionMt. Kinley is a strategy consulting firm that divides its consultants intothree classes: associates, managers, and partners. The firm has been stable in size for the last 20years, ignoring growth opportunities in the 90s, but also not suffering from a need to downsize inthe recession at the beginning of the 21st century. Specifically, there have been—and areexpected to be—200 associates, 60 managers, and 20 partners.The work environment at Mt. Kinley is rather competitive. After four years of working as anassociate, a consultant goes “either up or out”; that is, becomes a manager or is dismissed fromthe company. Similarly, after six years, a manager either becomes a partner or is dismissed. Thecompany recruits MBAs as associate consultants; no hires are made at the manager or partnerlevel. A partner stays with the company for another 10 years (a total of 20 years with thecompany).A. How many new MBA graduates does Mt. Kinley have to hire every year?B. What are the odds that a new hire…