Learning in the class must be well planned, one of which to create learning instrumen that refer to the curriculum implementation. This research aim to produces mathematics learning (Syllabus, RPP, and LAS) using the problem based learning model in the linear two-variable equation system sucject. This research is a research and development (R&D) using the 4-D model. The research instrument was …
This final discusses the solution of triangular fuzzy number transportation problem. Parameter of transportation costs, the amount of supply and demand are fuzzy numbers. The fuzzy zero suffix method is used to find the minimum solution to the triangular fuzzy transportation problem. The final result of the calculation of the fuzzy zero suffix method is to change the solution fuzzy number …
This nal project discusses the solution of transportation problem using the me- thod of Total Opportunity Cost Matrix-Minimal Total (TOCM-MT method). TOCM-MT method is used to determine the basic solution with the total cost of better mechanism and also to achieve similar values and approach to the opti- mal solution. TOCM-MT method obtains more minimal costs. An illustration as the sampl…
This final project discusses the dynamic effect of the greenhouse by modeling the shape of the earth like a rock. It is followed by discussing the effect of solar radiation on the model. Furthermore, the model is developed by adding an atmospheric layer to the first model obtained and analyzing the effect of solar radiation on this modified model. This final project is a review of part of a…
This final project discusses the predator-prey model with double predation. This model uses a system of nonlinear equation from the classic Lokta-Volterra model by adding one compartment, namely predator II. The solutions of the model are categorized into three categories which represent a three - plane coordinate system. This model has two equilibrium point, namely the origin point and po…
This final project discusses the diagonalization of a matrix triangular fuzzy numbers in interval form. Negative positive triangular fuzzy number with the concept on geometrical area can be used to determine eigen values and eigen vector of matrix triangular fuzzy numbers in interval form matrix and needed arithmatic operation that have been modified which refers to eigenvalues and eigenve…
This final project discusses the inventory model with shortage in triangular fuzzy numbers. The inventory model used is the EOQ model. The optimal solution of the model is achieved by using the Kuhn-Tucker conditions. Furthermore, the obtained Kuhn-Tucker conditions are formed into nonlinear programming so that the best decision is obtained in solving the EOQ problem. Thus the average valu…
We discuss a the system of absolute value equations as a family of parameterized smooth equations and propose a smoothing Newton method to solve this class of problems. Proved that the method is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical result demonstrate that the method is efective. This article is a review of the article Jiang [Ad…
ABSTRACT This nal project discusses a new iterative method for multiple roots of nonli- near equation which is free from second derivatives. Analytically it is shown that the method is of order three for a multiple roots and requires one function evaluation and two evaluations of rst derivative of function for each iteration. Numerical computations show that the new method gives the smal…
ABSTRACT This nal project discusses a transportation problem of the pentagonal fuzzy numbers using with the max-min method. This method is used to nd the initial base solution. Then to test the optimization and nd the optimal solution used the simplex transportation method. The solution is compared with the Vogel's approximation method. Based on the comparison of the two method, it is …
ABSTRACT This final project formulates the term life insurance premium with a uniform assumption for multiple decrement cases limited by two cases. Premium calculation is obtained by determining the life annuity first and the single premium value based on uniform assumptions. Life annuity and annual premiums are settled by first determining the insurance participant’s probability of exit…
ABSTRACT This final project discusses the premium of reserves of last survivor term life insurance based on premium sufficiency method for two persons. The calculation of this reserve is obtained by determining the single premium, annual premium, gross premium and life annuity with use at the constant force assumption. The premium is obtained by determining the life annuity and single prem…
ABSTRACT This nal project discusses the maximum ow using the Ford-Fulkerson al- gorithm and linear programming. Maximum ow problem solving using the Ford-Fulkerson algorithm is limited to capacity constraints, while solving using linear programming can be used for various kinds of constraints. At the end of the discussion, a maximum ow problem is given which is solved by using both …
ABSTRACT This nal project discusses some properties of decient perfect numbers, namely, every odd perfect numbers has a decient perfect numbers. Then there are odd perfect numbers and Descartes numbers from the decient perfect numbers. This is a review of article from Holdener dan Rachfal [The American Mathematical Monthly, 126 (2019), 541-546]. Keywords: Prime numbers, sigma function…
ABSTRACT This final projects discusses the trapezoidal fuzzy numbers transportation problem with mixed constraints. The cost coefficient is a fuzzy number that appears because there is uncertainty in costs that cannot be predicted due to several factors. The solution to the trapezoidal fuzzy number transportation problem uses the best candidate method (BCM) and the Vogel’s approximation …
ABSTRACT This final project discusses the mathematical modeling of a production planning using the preemptive goal programming method for priority based decision making. This problem aims to optimize the production planning by meeting the specified constraints and minimizing deviations from each goal to be achieved, based on the five types of best seller bread, production profits, producti…
ABSTRACT This nal project discusses the solution of assignment problem in the form of triangular fuzzy numbers that converted into crisp numbers, by using centroid method as ranking function. Then, the assignment problem in the form of crisp numbers is completed by using the Hungarian method, so that the solution that obtained from this method is used to properly place workers in order to…
ABSTRACT This nal project discusses the development of Japanese theorem for cyclic pentagon. The method is used to construct the diagonal from each point of the cyclic pentagon, so that three triangles are formed. Then it shows that the sum of incirle's radius of three triangles from the diagonal of cyclic pentagon is equal to the sum of incircle's radius of three triangles from diagonal …
ABSTRACT This final project discusses the existence of the perfect powers obtained by the result of the addition and subtraction of two Fibonacci numbers, namely and under the condition . In the case of , the addition or subtraction of and gives a product of and with and under the condition of or . Then the product of and is the perfect power in the form of with , a…
ABSTRACT This nal project discusses the properties of BN -algebra, the relationship BN - algebra with B -algebra, BF -algebra and Coxeter algebra. These properties are proved by using the binary operations contained in the group. This nal project is a review of article of Kim dan Kim [Kyungpook Mathematical Journal, 53 (2013), 175-184]. Keywords: BN-algebra, B-algebra, BF-algebra, Coxet…