Judul: Formulation of Coffee Bandrek Drink in PT Liza Herbal International. S
Abstrak: Bandrek merupakan minuman herbal tradisional yang terbuat dari rempahrempah dan tanaman herbal berupa jahe merah, cabai jawa, kayu manis, dan cengkih. Penelitian bertujuan menghasilkan produk bandrek kopi tanpa ampas yang disukai konsumen dengan melihat pengaruh rasio jahe dengan gula aren dan penambahan kopi. Metode yang digunakan yaitu metode kuantitatif. Penelitian dilakukan dalam beberapa fase, yaitu fase desain keteknikan, fase eksplorasi, fase pendefinisian masalah, fase ideasi, fase pengembangan prototipe serta fase validasi. Penelitian ini menghasilkan prototipe berupa produk bandrek kopi yang disukai dengan formula 50 gram jahe, 8 gram rempah, 40 gram gula pasir, penambahan gula aren sebanyak 13% dan penambahan kopi sebanyak 1,7%. Formula ini memenuhi syarat mutu SNI. Hasil pengujian masalah dan solusi menghasilkan formula terbaik dengan kemasan baru yang lebih disukai konsumen, proses produksi yang efisien, tata letak produksi yang efisien, dan hasil analisis usaha bandrek kopi yang dinilai layak berdasarkan aspek finansial karena memiliki nilai B/C ratio >1. Biaya investasi awal akan kembali dalam jangka waktu 2 tahun 7 bulan 13 hari, waktu ini kurang dari umur ekonomis alat selama 5 tahun., Bandrek is a traditional herbal drink made from spices and herbal plants in the form of red ginger, javanese pepper, cinnamon, and cloves. The aim of this research is to produce a coffee bandrek without pulp that is preferred by consumers by looking at the effect of the ratio of ginger to palm sugar and the addition of coffee. The method used is a quantitative method. The research was conducted in several phases, namely the engineering design phase, the exploration phase, the problem definition phase, the ideation phase, the prototype development phase and the validation phase. This study produced a prototype in the form of a preferred coffee bandrek product with a formula of 50 grams of ginger, 8 grams of spices, 40 grams of granulated sugar, the addition of 13% palm sugar and the addition of 1.7% coffee. This formula meets the national quality requirements. The results of testing the problems and solutions produce the best formula with new packaging that is preferred by consumers, an efficient production process, an efficient production layout, and the results of an analysis of the coffee bandrek business which are considered feasible based on the financial aspect because it has a B/C ratio >1. The investment cost will return within 2 years 7 months 13 days, this time is less than the economic life of the tool 5 years.
Keyword: bandrek, jahe merah, kopi, minumal herbal, minuman tradisional, coffee, herbal drink, red ginger, traditional drink

Judul: Bandrek Honey Beverage Formulation at PT Liza Herbal International
Abstrak: Dalam perindustrian, product life cycle dapat digunakan untuk menentukan fase hidup dan kebutuhan suatu produk. Dari product life cycle bandrek PT Liza Herbal International, diketahui bahwa bandrek sedang memasuki fase decline atau penurunan penjualan. Oleh karena itu, berdasarkan penyebabnya, dibutuhkan inovasi berupa formulasi untuk meningkatkan citra dan penjualan bandrek. Sebanyak 13 formulasi dengan bahan baku dan metode yang berbeda menghasilkan 1 formula dengan bahan baku dan metode produksi tetap. Formula tersebut dikembangkan menjadi 9 formula bandrek dengan konsentrasi jahe dan gula aren berbeda, kemudian dianalisis secara proksimat dan organoleptik. Hasil penelitian menunjukkan 1 formula yang paling disukai panelis dengan karakteristik fisikokimia terbaik. Formula tersebut kemudian divariasi menggunakan madu bubuk untuk memperluas pangsa pasar dan memperkaya manfaat bandrek. Penelitian ini divalidasi dengan analisis kelayakan finansial dan dilengkapi dengan saran tata letak area produksi., In industry, the product life cycle can be used to determine the life phase and needs of a product. From product life cycle of PT Liza Herbal International’s bandrek, it is known that bandrek is entering a decline phase or sales decline. Therefore, based on the cause, innovation in the form of formulations is needed to improve the image and sales of bandrek. A total of 13 formulations with different raw materials and methods resulted in 1 formula with fixed raw materials and production methods. The formula was developed into 9 bandrek formulas with different concentrations of ginger and palm sugar, then analyzed proximately and organoleptically. The results showed 1 formula that was most preferred by the panelists with the best physicochemical characteristics. The formula was then varied using powdered honey to expand market share and enrich the benefits of bandrek. This study was validated by a financial feasibility analysis and equipped with suggestions for the layout of the production area.
Keyword: bandrek, formulasi, product life cycle, formulation

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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