This paper discusses the combination of forecasting methods and linear programming to make a decision. Both of the methods are used to predict the sales of bakery products and to determine the best and most efficient product combinations. The forecasting methods used are moving average and exponential smoothing. Then a comparison is carried out for both forecasting methods to select the bes…
This research is inspired by the implementation of the 2013 curriculum in education which requires teachers to prepare learning well. One form of preparation carried out by the teacher is preparing learning tools that support the implementation of the 2013 curriculum, including mathematics. The results of observations and analysis conducted by researchers on the learning tools used by teachers …
This study is motivated by the implementation of the 2013 Curriculum which requires the teacher to prepare the design of learning activity before conducting the learning process. Learning plans can be undertaken by developing learning media that is in accordance with the guideline of 2013 curriculum in order to achieve the objectives of learning mathematic. One of the aims of learning mathemati…
This research aims to produce digital learning media assisted with worksheet on flat side geometry for VIII grade students of Junior High School degree that are valid and practical. The development model used in this research is the ADDIE model which consists of five steps, that is analysis, design, development, implementation, and evaluation. The instrument used in this research is a validatio…
This research aims to produce mathematics learning instrument which includes syllabus, learning implementation plans (RPP) and student activity sheets (LAS) by using Problem Based Learning on algebraic form material for the sevemth grade of SMP/MTs that are valid and practical. This research development model is a 4-D model which consists of the stages of define, design, development, and dissem…
The research background is the importance of mathematics learning devices as a form of learning planning prepared by the teacher in order to achieve learning objectives, but the mathematics learning devices used by the teacher still have a mismatch with demands of the 2013’s curriculum. This research is aimed to produce a learning devices using the discovery learning model that is categorized…
This research is a class action research which aimed to improve learning process and increase student’s the mathematics learning outcomes at class VII.8 SMP Negeri 25 Pekanbaru by implying Problem Based Learnin model (PBL). The subjects of this research were VII.8 grade student’s of SMP Negeri 21 Pekanbaru in the academic year 2019/2020 wihich total number of participants were 39 studen…
This class action research aims to improve learning process and increase the mathematics learning outcomes by implying Problem Based Learning model. Subjects of this research were the students of grade VII2 SMP Negeri 42 Pekanbaru in the academic year 2019/2020 total number of participant are 38, consisting of 18 boys and 20 girls with heterogeneous academic achievement. This research has two c…
This class action research aims to improve learning process and increased the mathematics learning outcomes by implying Problem Based Learning model. Subjects of this research were the students of grade VII.5 SMP Negeri 4 Pekanbaru in the academic year 2019/2020 total number of participant are 39 with heterogeneous academic achievement. This research have two cycles, each have four stages: plan…
This final project discusses Napoleon’s outer and Napoleon’s inner in general on triangle. Each vertex is connected from a triangle which is built based on the sides of the original triangle, so that a new triangle is formed, namely Napoleon’s outer and Napoleon’s inner with certain conditions. The proof is done using the concept of similarity. This final project is a modification o…
This nal project discusses how to nd the eigenvalues and eigenvectors of matrix trapezoidal fuzzy numbers. Trapezoidal fuzzy numbers are expressed as negative-positive denition. The goal is to determine the algebraic operations that are constructed on the result of multiplying the trapezoidal fuzzy numbers, and are used to determine the eigenvalues and eigenvectors of trapezoidal fuzzy …
This nal project discusses the solution to a systems linear equations in complex fuzzy numbers. In solving complex fuzzy number, arithmetic is used in numbers fuzzy and arithmetic is also usesd in complex fuzzy number. This system of equation is converted into 2n 2n matrix form. Then the solution of the equation are obtained using Gauss-Jordan elimination. Keywords: Fuzzy numbers, compl…
This final project discusses the stability of the predator-prey model using the Holling-II and threshold harvesting functions against predator. Three of five equilibrium points obtained are stable as seen from the eigenvalues of the system linearity matrix. At the end of the discussion, the model behavior for the two equilibrium points generated with threshold harvesting shows that the solu…
This final project discusses how to apply sensitivity analysis to the triangular fuzzy number linear programming. Sensitivity analysis is used to determine the changes in the triangular fuzzy number on the coefficient of the objective function, the changes in the value of the right side of the constraint function and the addition of new constraints so that the optimal solution can be mainta…
The ratio estimators studied here are ratio estimators for population mean of simple random sampling by using information of correlation coefficient, second quartile, quartile deviation and decile mean. Each estimator is biased estimator. Furthermore, to obtain an efficient estimator is carried out comparing the MSE of each estimator with the simple ratio estimator used by Cochran. Then it …
This final project discusses a decreasing sequence (an) of nonnegative terms, the- re exist subsequences (nk) of (n) such thatP1k=1(nk+1−nk)ank andP1n=1 an ha- ve the same convergence. Then for P1n=1 an converges if and only if P1k=1 qkaqk converges for 1 < q ∈ N. Using these results, an extension of the ratio test is formed. Keywords: Sequence, series, convergency, divergency
This final project discusses the sensitivity analysis of transportation problems in triangular fuzzy numbers. The optimal solution of the transportation problem is obtained after converting the triangular fuzzy number in the transportation problem into a crisp number. When the optimal solution obtained remains the same for a long time, a sensitivity analysis is carried out to determine chan…
This nal project discusses the determinant of interval matrix with the calculation used is a combination of some interval arithmetic which has a shorter interval value than others. Assuming that a shorter interval value is an optimal value. The method used in determining the determinant of interval matrix is the modied Crout's method in the article of Nirmala and Ganesan [Journal of Phys…
This nal project discusses the modication of the fourth order multistep Adam- Bashforth and Adam-Moulton method by changing the integral boundaries of [xn; xn+1] to [xn−2; xn+1] to solve initial value problems. In generally, the com- parison results show that the numerical solution obtained with the modication of the fourth order multistep Adam-Bashforth and Adam-Moulton method has an…
This research is a development purposed is to produce mathematics learning devices such as syllabus, lesson plans, and student worksheet by using discovery learning on curved face three dimensional (cylinder, cone, and ball) material for the 9th grade of junior high school. This research is motivated by the incompatibility instruments which arranged by teacher based on 2013 Curriculum. The…