Judul: Scale Up Production Design of Kombucha Cascara KTH Cibulao
Abstrak: Kombucha cascara merupakan produk minuman olahan cascara atau kulit kopi kering yang dapat menjadi solusi untuk mengatasi 2400 kg limbah kulit buah kopi yang dihasilkan Kelompok Tani Hutan Cibulao setiap tahunnya. Kombucha merupakan minuman ringan hasil fermentasi yang tengah meningkat popularitasnya baik secara global maupun nasional karena rasanya yang enak dan potensi kesehatannya. Komersialisasi kombucha cascara di Indonesia dapat menjadi prospek yang menjanjikan dengan perencanaan produksi yang memadai. Kombucha cascara yang dirancang sejak produta sebelumnya membutuhkan perbaikan formula sebelum digandakan skalanya (scale up) untuk keperluan komersialisasi. Penggandaan skala produksi menggunakan acuan produksi skala laboratorium yaitu kombucha cascara dengan basis produksi 9 liter (L) dan lama fermentasi 9 hari yang menghasilkan 27 botol kemasan 250 ml serta cycle time 8,1 jam. Kapasitas produksi scale up menjadi 414 botol kemasan 250 ml per batch produksi yang dihasilkan dari 15 wadah fermentasi 9 L. Setiap bulannya dioperasikan 2 batch produksi dengan total hari produksi per batch selama 11 hari. Sejumlah 20,1 kg starter kombucha yang dihasilkan dari batch produksi genap akan dijual sebanyak 67 pak/bulan untuk mengendalikan kapasitas penyimpanan. Peralatan dan mesin yang digunakan pada titik fokus scale up adalah sterilizer, panci, kompor 2 tungku, mixer, dispenser kaca, rak 5 tingkat, upright chiller, papan infraboard, serta dispenser galon. Standar kegiatan produksi, lokasi kegiatan, dan penanggung jawab setiap kegiatan produksi disusun dalam Standar Operasional Produksi., Kombucha cascara is a beverage made from cascara, dried coffee skin and pulp, offering a solution for 2400 kg of coffee cherry waste produced annually by Kelompok Tani Hutan Cibulao. Kombucha undergoes a fermentation process which resulting in a sweet, sour, and carbonated beverage. Due to its pleasant taste and potential health benefits, kombucha is gaining popularity globally and nationally. The commercialization of kombucha cascara in Indonesia holds promising prospects with proper production process planning. Kombucha cascara, initially designed by previous produta team, requires formula improvement before scaling up for commercial purposes. Scaling up production is based on chosen formula of laboratory scale kombucha production with a production basis of 9 liters (L) and fermentation period of 9 days, yielding in 27 bottles of 250 ml with a cycle time of 8,1 hours. The capacity of production scales up to 414 bottles of 250 ml per production batch, yielded from 15 fermenting vessels of 9 Ls each. Two production batches are operated monthly, with each batch requiring a total of 11 production days. Kombucha starter worth of 20,1 kg from even numbered production batches will be sold for 67 packs every month to control storage capacity. The equipments utilized for focal points of scale up include sterilizer, pot, 2 burner stove, mixer, glass dispenser, 5 tier rack, upright chiller, infraboard panel, and plastic dispenser. Standard of production activity, activity locations, and responsible workers for each production activity are outlined in the Standard Operating Procedure.
Keyword: Kombucha cascara, product reformulation, scale up, mass balance, production equipment, production standardization

Judul: Desain Model Bisnis Kanvas dan Analisis Finansial  Bisnis Kombucha Cascara KTH Cibulao
Abstrak: Cascara kombucha is a beverage produced by fermenting sweet cascara with SCOBY. This design project aims to develop a small-scale cascara kombucha business that has been formulated in the previous design project with the Forest Farmer Group (KTH) Cibulao. The designed solution is to scale up the kombucha production to a capacity of 828 bottles of kombucha per month, targeting consumers in the Jabodetabek area aged 20-49 years old. The product is sold for IDR25.000 (margin 150.93% of the cost of production IDR9.963) to final consumers and IDR20.000 (margin 100.74%) to re-sellers. CasTIN cascara kombucha 250 ml is positioned as a refreshing drink for consumers. The layout design for the production space of 60.04 m2 is done using the Corelap method, considering production capacity, minimal costs, minimal land area, and production process flow. Shelflife testing indicates that the product is good for consumption for approximately 8 months (storage temperature 4-10°C) and 5 days (room temperature storage). The product is packaged in tightly sealed glass bottles to withstand the pressure of CO2 gas resulting from fermentation activity that may still occur. The business process is modeled using BPMN involving KTH Cibulao as cascara supplier, CasTIN as industry or manufacturer, and consumers. The results of the financial feasibility analysis show that the business is feasible to run with the criteria values of NPV (IDR3.115.137.024) > total capital (IDR64.692.595), Net B/C 94.15, IRR 399%, Payback Period of 11 months, ROI 430.79%, and BEP units at 172 bottles and BEP revenue of IDR1.725.884. The profit sharing from the annual net profit will be distributed to the cascara kombucha business CasTIN 85% and to the Agroindustrial Technology Department of IPB University at 15%.
Keyword: Kombucha, scale up, shelf life, cascara, business process

Judul: igenvalues and Eigenvectors of Tridiagonal Matrix with Non Constant and Recurrent Diagonal Entries.
Abstrak: Matriks tridiagonal adalah suatu matriks yang mempunyai entri-entri bernilai nol kecuali pada diagonal utama, di bawah diagonal utama (subdiagonal) dan di atas diagonal utama (superdiagonal). Entri pada diagonal utama tidak konstan dan berulang. Setiap entri pada matriks tridiagonal ini adalah bilangan kompleks. Dalam karya ilmiah ini, akan dibuktikan 3 teorema untuk menentukan nilai eigen dengan 2 kasus dan 1 teorema untuk menentukan vektor eigen. Teorema pertama menentukan polinomial karakteristik dari matriks tridiagonal. Polinomial karakteristik dari matriks tridiagonal tersebut digunakan untuk menentukan nilai eigen pada teorema kedua dan ketiga serta menentukan vektor eigen pada teorema keempat
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