# Mathematics

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Item CADANGAN ZILLMER ASURANSI JIWA DWIGUNA MENGGUNAKAN DISTRIBUSI FRECHET(Elfitra, 2023-11) Prahasiwi, Syifa WahyuniShow more Life insurance is a protection effort provided by the insurer against risks to the insured’s life that will arise from an unpredictable event. Insurance companies need to calculate reserves to prepare funds when participants request a claim. Zillmer’s reserves are modified reserves that are calculated using prospective reserves and a zillmer rate of α.This final project aims to determine Zillmer reserve of endowment life insurance for two insurance participants who are x years old by using Frechet distribution. The parameters in the Frechet distribution were estimated using maximum likelihood estimation and then determined by a Newton-Raphson iteration method. The calculation of this Zillmer’s reserve is obtained by using the prospective reserve and Zillmer’s rate. The solution of this problem is obtained by determining the initial life annuity temporary, single premium, and annual premium, then the Zillmer’s reserve formula is obtained based on the distribution of Frechet. Zillmer’s reserves for endowment life insurance using the Frechet distribution is smaller than Zillmer’s reserve for endowment life insurance using the Indonesian Mortality Table 2011Show more Item METODE ITERASI BEBAS TURUNAN DENGAN TEKNIK SPLITTING UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(Elfitra, 2023-11) Hudiyani, SefiyaShow more This article discusses a new iterative method that is derivative-free and is obtained by converting a single nonlinear equation to a system consisting of two equations. By using the splitting method, a sufficient conditions will be obtained that must be met for the convergence of this method. The convergence analysis shows that the proposed method has a third order convergence for certain parameters. Numerical comparisons between the proposed method and some other third order methods using several examples shows that the proposed method can be used as an alternative method for solving nonlinear equation.Show more Item PENGEMBANGAN MIXTILINEAR INCIRCLE DAN EXCIRCLE PADA BISEKTOR SUDUT SUATU SEGITIGA(Elfitra, 2023-11) Jefri, SamuelShow more We discuss a development of mixtilinear incircle and excircle in bisectors of triangle. The development carried out demonstrates the relation that forms between the radii of mixtilinear incircles and excircles that can be constructed on the angle bisectors of 4ABC. In each triangle, three di erent mixtilinear incircles and excircles are formed. The relation between the radii of mixtilinear incircles and excircles on the angle bisectors of 4ABC is such that the ratio of the product of their radii to the angle they form is equal to the ratio of the bisecting lines that form them.Show more Item AKAR KUADRAT DARI MATRIKS KUADRAT ORDE 3(Elfitra, 2023-11) Syahreza, Robby FerikoShow more A new approach is presented in this article with the purpose of calculating the square roots of a quadratic matrix order 3. Determination of the explicit formula for each square roots of quadratic matrix order 3 can be determined by applying the Cayley-Hamilton Theorem to its characteristic polynomial. Some examples are given in the application of the explicit formula to determine the square roots of a quadratic matrix order 3.Show more Item PENYELESAIAN MASALAH INVENTORI MENGGUNAKAN MODEL EOQ MULTI-ITEM DAN SIMULASI MONTE CARLO(Elfitra, 2023-11) Juwita, Rahmi SeptiaShow more This article discusses the solution of inventory problems using EOQ multi-item model and Monte Carlo simulation to determine problem solving techniques that can be used to managing inventory. EOQ multi-item model gives an optimal solution so that it can be saving the cost of inventory. Monte Carlo simulation is an alternatives technique that are associated with uncertainty or probability which is in the solution used past data and variable random to predict inventory in the future. Therefore, EOQ multi-item model and Monte Carlo simulation are problem solving technique that can be used to managing inventory.Show more Item PENERAPAN TEORI PERMAINAN DALAM MENENTUKAN STRATEGI OPTIMAL MEDIA SOSIAL DENGAN PEMROGRAMAN LINEAR DAN ALGORITMA BROWN(Elfitra, 2023-11) Damayanti, OlifiaShow more This article discusses the application of game theory on social media competition using linear programming and Brown’s algorithm. This problem aims to determine the optimal strategy for each social media. The social media in this study are Instagram, Tiktok, and Twitter. Alternative strategies are information strategy, communication strategy, promotion strategy, and entertainment strategy. Based on the survey conducted, the survey results can form a matrix payoff. Matrix payoff of m×n size with m, n ≥ 2 can be solved by Brown’s algorithm and domination. The domination is used to reduce the matrix of m × n size becoming smaller, then the matrix can be solved by linear programming using the simplex method. Linear programming and Brown’s algorithm gives the same results, optimal strategy for Instagram are communication strategy and entertainment strategy. The optimal strategies for Tiktok are information strategy, promotion strategy and entertainment strategy. The optimal strategy for Twitter are information strategy and entertainment strategy.Show more Item METODE ITERASI ORDE LIMA MENGGUNAKAN FUNGSI BOBOT DAN BASINS OF ATTRACTION(Elfitra, 2023-11) Oktarina, OktarinaShow more This article discusses a two-step iterative method for solving nonlinear equations. This method is obtained by modifying Newton’s method using a weight function. Analytically, it is shown that using Taylor expansion and geometric series, this iter- ation method has a convergence order of five and requires four function evaluations for each iteration. This fifth order iteration method has an efficiency index of 1.495. Numerical computations show the new method is comparable to other fifth-order methods discussed. This article also discusses basins of attraction, namely a visual depiction of the dynamic behavior of an iteration method for nonlinear equations from various starting points.Show more Item MANFAAT PENSIUN NORMAL DENGAN METODE ENTRY AGE NORMAL BERDASARKAN DISTRIBUSI RAYLEIGH(Elfitra, 2023-11) Ainun, NurShow more The welfare of workers at retirement age is an important factor in ensuring ful llment of needs in old age, especially workers who work for a company or a government agency. Workers must have an early plan that can guarantee future welfare when entering retirement age. Given the economic development and technological advances that will trigger an increase in needs, a worker will certainly not always be able to work well especially after reaching a certain age. Workers' productivity will decline and workers will enter retirement age where needs still exist and will continue to exist while after retirement workers no longer get income from their previous jobs. One solution that can be done is to join a pension fund program. This research aims to determine normal retirement bene ts, normal contributions and actuarial liabilities with the normal entry age method based on the Rayleigh distribution. The parameters in the Rayleigh distribution were estimated using maximum likelihood estimation and then Maple 13 software was used to obtain the estimation results.The solution of problem is obtained by determining the probability of death, initial life annuity temporary, bene ts, normal contributions and actuarial liabilities with the normal entry age method and then formula is obtained based on the distribution of Rayleigh. The amount of pension bene ts, normal contributions and actuarial liabilities obtained by using the normal entry age based on the Rayleigh distribution is smaller than the case study conducted at Pt.Taspen Pekanbaru branch.Show more Item OPTIMISASI PRODUKSI MENGGUNAKAN PROGRAM LINEAR MULTI OBJECTIVE FUZZY DENGAN SUMBER DAYA FUZZY DAN KENDALA FUZZY(Elfitra, 2023-11) Putri, Luthfiyah UtamiShow more This paper discusses the mathematical modeling of linear programming problems production using the fuzzy multi objective linear programming method. This problem aims to optimize production by fulfilling constraints determined to achieve the goal of maximum profit and more efficient use of time. Mathematical models in this problem is designed using the LINGO 19.0 application. Computational results shows that the fuzzy multi objective linear programming method is more efficient used to achieve goals.Show more Item PENGGUNAAN MODEL LOKASI-ALOKASI DALAM PENGOPTIMALAN JUMLAH DAN LOKASI POS PEMADAM KEBAKARAN(Elfitra, 2023-11) S, Erfa Julia.Show more This articel discusses the application of location-allocation model in optimizing the number and location of fire stations in Pekanbaru City. This quantitative locationallocation model is solved by formulating the Set Covering Location Problem (SCLP) model and the p-median problem model. The mathematical model in this problem is solved using the LINGO 18.0. Computational results show that this location-allocation model can determine the minimum number of fire stations, location of fire stations, and the better allocation of each subdistrict to the fire stations.Show more Item KELUARGA BARU METODE ITERASI OPTIMAL ORDE EMPAT UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(Elfitra, 2023-11) Liana, Ema VikaShow more This article project discusses a new family of optimal fourth-order iterative method to solve a nonlinear equation. Analytically using the Taylor expansion and geometric series that the iterative method has a convergence order of four and efficiency index is 1.587. Comparisons of computational tests shows that a new family of optimal fourth-order iterative methods can be used as an alternative in solving nonlinear equations.Show more Item METODE HOMEIER-NEWTON DENGAN ORDE KONVERGENSI ENAM UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(Elfitra, 2023-11) Sari, Dhita Aulifia BestaShow more This article discusses a three-step iteration method obtained from the third-order Homeier method by adding a Newton step and approximating the derivative in last step of iteration by using linear interpolation. Convergence analysis shows that the resulting method has a convergence order of six with an efficiency index of 1.5651. Computational tests concluded that this method can be used as an alternative method in solving nonlinear equations.Show more Item MERUMUSKAN POLINOMIAL KARAKTERISTIK DARI MATRIKS LUCAS-SYLVESTER-KAC(Elfitra, 2023-11) Damanik, Desy AriantyShow more This article discusses the formula determinant for the Lucas-Sylvester-Kac matrix of order n × n. In addition, this final project also aims to show how the Lucas- Sylvester-Kac matrix satisfies matrix centrosymmetric form for determine charac- teristic polynomial,eigenvalues of Lucas-Sylvester-Kac matrix of order n × n. This final project also considers two cases, namely when the Lucas-Sylvester-Kac matrix has even order n and when the Lucas-Sylvester-Kac matrix has odd order n.Show more Item MENENTUKAN LOKASI DAN JUMLAH POS PEMADAM KEBAKARAN DENGAN MENGGUNAKAN MODEL SET COVERING PROBLEM(Elfitra, 2023-11) Ramadhani, Desri AnnisaShow more This article discusses the use of the Set Covering Problem (SCP) model in determining the optimal location and number of fire stations in Pekanbaru City. The SCP model includes Location Set Covering Problem (LSCP) and Maximum Covering Location Problem (MCLP). Problems in this model are solved using the LINGO 18.0 application. Based on the LSCP model, the minimum number of fire station locations is eight fire stations. The results of the LSCP model are used to formulate the MCLP model to improve fire station services. The SCP model provides optimal results in determining the location and number of fire stations.Show more Item ANALISIS DINAMIKA MODEL PREDATOR-PREY TIPE LESLIE DENGAN RESPON FUNGSIONAL YANG MENINGKAT(Elfitra, 2023-11) Sintika, Delly ManjaShow more This article discusses the interaction between two populations namely prey and predators, which is then investigated using the Leslie type with an increased functional response. In the observed model, it is shown that the model has a predator-free equilibrium point and a positive equilibrium point. It is indicated that the model has saddle-type stability at the predator-free equilibrium point and several stability at the positive equilibrium point, one of which is global asymptote stability as determined using the Dulac function. Simulations of the model are carried out to describe the dynamics and stability of the equilibrium points using certain parameters.Show more Item ALTERNATIF PROSES DIAGONALISASI MATRIKS BILANGAN FUZZY TRIANGULAR(Elfitra, 2023-11) Sibarani, David RakelShow more This article discusses the alternative diagonalization process on the triangular fuzzy number matrix of size n×n in parametric form. Many forms of arithmetic operations have been given by the author, especially triangular fuzzy numbers. For addition, subtraction and scalar multiplication operations there is not much difference while for multiplication, division and inverse there are many ways. However, the algebraic operations offered have some drawbacks for example, for any triangular fuzzy number ˜p = (p, α, β), does not necessarily apply ˜p(r) ⊗ 1 ˜p(r) = ˜i(r) . In this article, an alternative arithmetic operation will be used for the multiplication, division and inverse operations of triangular fuzzy numbers by using the midpoint concept. This midpoint concept is then used to determine the eigenvalues and eigenvectors as well as the inverse matrix of triangular fuzzy numbers. Meanwhile, to determine the cofactor of the triangular fuzzy number matrix using ˜ Cij(r) = [−1,−1]i+j ⊗ ˜Mij(r).Show more Item ANALISIS DINAMIKA MODEL PREDATOR-PREY DENGAN PERLINDUNGAN PREY DAN FEAR EFFECT(Elfitra, 2023-11) Mardhya, Azura FarrastShow more This article discusses the dynamics of the predator-prey model with prey refuge and considers the effect of fear. The observed model has four equilibrium points where two points are unstable and other points are stable under certain conditions. Simulation of the model is carried out with spesific parameters to describe the behavior and stability of the equilibrium points. Based on results of simulation, the influence of fear effect has a negative impact on the prey population and leads to extinction. Meanwhile, for the case with a constant rate of fear, prey refuge has a positive impact on the coexistence of predator and prey.Show more Item METODE ITERASI BEBAS TURUNAN KEDUA OPTIMAL DENGAN ORDE KONVERGENSI EMPAT UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(Elfitra, 2023-11) Kurniawan, ArifinShow more This article discusses the optimal second derivative-free iterative method to solve nonlinear equations obtained by approximating the second derivative of the Noor- Noor-Momani method using quadratic and cubic polynomials. Analytically, this iterative method has an order of convergence four and its efficiency index is 1.5874. The computational test shows that the resulting method can be used as an alternative method for solving nonlinear equations.Show more Item TURUNAN FRAKSIONAL RIEMANN-LIOUVILLE DARI f(x) = sin(kx)(Elfitra, 2023-10) Erlianto, YogaShow more This article discusses fractional derivatives of trigonometric functions with Riemann- Liouville fractional derivative and related with gamma functions. The fractional derivative is denoted by D( )f(x) where is a fractional number greater than 0 and x is a variable. The fractional derivative of a trigonometric function is obtained by using some properties of the gammaShow more Item ANALISIS PERBANDINGAN METODE FORWARD DAN BACKWARD DALAM PEMODELAN REGRESI LINEAR BERGANDA(Elfitra, 2023-10) Tahir, Yofi Kurnia; Efendi, RustamShow more The issue of health insurance costs has become a major concern in the healthcare system in the USA. Determining the accurate health insurance cost is crucial for individuals and families who rely on health insurance for financing their healthcare. This research aims to compare the most effective methods for determining health insurance costs using variable selection methods in multiple linear regression models. The variable selection methods used are forward selection and backward elimination. Based on the application in the regression model, the forward selection method yielded dan RMSE values of 79.68% and 2024.295, respectively. The backward elimination method produced dan RMSE values of 96.77% and 807.175, respectively. The most effective variable selection method for determining health insurance costs in this case is backward elimination.Show more