ABSTRACT This final project discusses the new iterative method using weight function and Jarratt’s method for solving nonlinear equation. The convergence analysis using Taylor expansion and geometric series show that the proposed method has a fourth order convergence with efficiency index is 1.587. The numerical comparisons of the method to some other fourth order methods using several examp…
ABSTRACT This nal project discusses the development of the mixtilinear incircle on the triangular trisector of a triangle. The development carried out is to show the relationship formed between the radii of the mixtilinear incircle which can be constructed from the triangles on the trisector of angle 4ABC. Each triangle is formed by three dierent mixtilinear incircles. The relationship b…
ABSTRACT This final project discusses three comparisons of new iteration methods, Arithmetic Newton, Harmonic Newton, and Geometric Newton, to solve nonlinear equations. The process of forming these methods uses the equation of the tangent line approximated by arithmetic mean to produce the Arithmetic Newton method, and the harmonic mean for the Harmonic Newton method, and the geometric m…
ABSTRACT This nal project discusses the comparison of three new iterative methods, the trapezoidal Newton method, the midpoint Newton method, and the modied midpoint Newton method, for solving nonlinear equations. The process of de- veloping these three methods involves using tangent line equations formed by integrals and approximated using the trapezoidal rule and midpoint. Conver- gen…
ABSTRACT This final project discusses the assignment problems. The assignment problem is then solved with the Hungarian method and modified Hungarian method for unbalanced cases with more officers than machines. Solving the unbalanced as- signment problem uses the Hungarian method and modified Hungarian method by is carried out reducing the rows and columns in the matrix until a single zer…
ABSTRACT This nal project discusses the direct product of GK-algebras and it's proper- ties. This nal project is to show that the direct product of two GK-algebras is also a GK-algebra. Then by applying the concept of direct product GK-algebras a so that generalization of direct product is obtained on homomorphisms, iso- morphisms, dan kernel GK-algebras. Keywords: GK-algebras, homomorp…
ABSTRACT This final project discusses how to determine the point of reordering on the EOQ model where there are defective goods. Inspection is carried out to distinguish defective goods from good goods. How to determine the reorder point, which is the average demand multiplied by a known and constant waiting time. Making an order before the inspection time is over, an order is made before …
ABSTRACT This nal project discusses some identities for sum of reciprocal generalized Fibonacci numbers (Gn) with n = k for a positive integer k as well sum of reciprocal generalized Fibonacci numbers (Gn) with n = 2k + 1 or n is positive odd integer and n = 2k or n is positive even integer for a positive integer k. Then by applying the oor function to the sum of reciprocal discussed, a…
ABSTRACT This final project discusses the annual premium on joint life and last survivor endowment life insurance for two insurance participants aged who are x and y years old by using Clayton copula. The solution of this problem is obtained by determining the term initial life annuity temporary and single premium for each status, then the annual premium formula is obtained based on the Cl…
ABSTRACT This final project discusses the simplex method is modified in the case of cubic programming minimization. Cubic programming is an optimization problem with a nonlinear function and linear constraint function. The technique used for solving cubic programming is to determine the value of the objective function z using the simplex method which has been modified based on the basic de…
ABSTRACT This final project discusses the EOQ model with price decreases. When suppliers decrease the selling price per item in the regular sales period, the optimal order quantity increases and gets optimal cost benefits. Furthermore, the method used in this inventory model is the algebraic method. Using algebraic methods where optimal custom order quantities and optimal cost benefits ar…
ABSTRACT This final project discusses the solution of transshipment problem using the simplex method of transportation. This discussion aims to determine the optimal solution of the transshipment problem by taking into account the freight cost coefficient. The initial process of solving this problem by illustrating how to change the form of fuzzy numbers into strict number forms using the …
ABSTRACT This final project discusses proposes a fuzzy Pythagoras approach with the zero point method for solving transportation problems with uncertain data. The approach combines fuzzy logic and the Pythagorean theorem to optimize resource allocation in transportation systems. The zero point method is utilized to find optimal solutions by considering the membership levels in fuzzy sets. …
ABSTRACT This nal project discusses the solution of multi-objective linear interval pro- gramming with exible fuzzy constraints using a two-phase approach. The objective function is in the form of interval. The solution to this problem is to converting the multi-objective function into a single objective function using the weighting method, then the interval number in the objective func…
ABSTRACT This nal project discusses the solution of the transshipment problem of trapezoidal fuzzy numbers using the max-min method. This method is used to nd the initial basis solution, then to test the optimality and nd the optimal solution using the transportation simplex method. The solutions obtained are compared with the Vogel approximation method. Based on the comparison of the …