This final project 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 geo- metric series, this iteration method has a convergence order of five and requires four function evaluations for each iteration. This fifth order iteration method ha…
This final project discusses the formula determinant and characteristic polyno- mial for the Lucas-Sylvester-Kac matrix of order n n. The solution is obtained by using the application matrix centrosymmetric form, and in 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. Characte- risti…
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 β.This final project aims to determin…
The welfare of workers at retirement age is an important factor in ensuring fulfillment 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 …
This final project discusses the application of location-allocation model in optimizing the number and location of fire stations in Pekanbaru City. This quantitative location-allocation 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. The completion of the SCLP m…
This final project 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 with a maximum travel time of 15 minute…
The pension fund program is a type of future planning that tries to assure a person’s safety and comfort in old age. This final project discusses the normal cost of the pension fund using the projected unit credit method in the case of multiple decrement. Based on data service table PT. Taspen Pekanbaru City Branch with three cases, namely normal retirement, withdraw ret…
This final project explains the application of game theory on social media com- petition 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 informa- tion strategy, communication strategy, promotion strategy, and entertainment str…
The final project discusses the properties of incline algebra and right derivation of incline algebra. The discussion includes the concept of relation, poset, dis- tributive lattice, boolean algebra, incline algebra, and semiring. The result of this project show the relationship right derivation of incline algebra with right derivation semiring. Keywords: incline algebra, right derivation, d…
This final project discusses about predator-prey model with Holling type-II functional response with the impact of fear and Allee effect in prey population. In the model observed, there are four equilibrium points in which three of them are stable under certain conditions. This model undergoes Hopf bifurcation at the positive equilibrium by taking the level of fear as bifurcation parameter. Si…
This final project discusses prime cyclic ideals on Gaussian integers and Ei- senstein integers over ring modulo n with a, b Zn. That is solved by using theorems related to the characteristics of prime cyclic ideals applied to the Ga- ussian ring of integers and the Eisenstein ring of integers. This characteristics show that Gaussian primes and Eisenstein primes are prime ideals. Keywords: P…
This final project discusses the Sylvester matrix of order (n + 1) (n + 1), the Sylvester matrix is a tridiagonal matrix that has main diagonal entries are real numbers, the upper subdiagonal entries are 1, 2, . . . , n while the subdiagonal entries the bottom is inversely proportional to the upper subdiagonal entry. Then calculate the spectrum and determinant of the Sylvester matrix by finding…
This final project discusses the solution of inventory problems using EOQ multi- item model and Monte Carlo simulation to determine problem solving techni- ques 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 Car- lo simulation is an alternatives technique that are associated with uncertainty or prob…