Judul: Optimasi Formula Minuman Sari Buah Nanas-Wortel Menggunakan Desain Mixture D-Optimal
Abstrak: Pasar minuman ringan Indonesia sudah tersaturasi dengan minuman yang sama, dengan sedikit variasi, seperti minuman teh kemasan Ready to drink (RTD) dan minuman ringan berkarbonasi. Minuman ringan dengan basis buah jarang ditemukan, dan lebih jarang lagi berdasarkan buah nanas. Penelitian ini bertujuan untuk menemukan formula optimal untuk minuman ringan berbasis nanas-wortel dengan menggunakan metode Response Surface Method (RSM) dengan desain mixture D-Optimal. Penelitian ini juga bertujuan mengukur kadar antioksidan dari formula optimal yang didapatkan dengan menggunakan metode DPPH. Formulasi menggunakan tiga variabel bebas dan lima variabel tetap, variabel bebas berupa jumlah ekstrak wortel (10-30%, bb), jumlah ekstrak nanas (15-35%, bb), dan jumlah gula (5-10%, bb). Variabel tetap berupa jumlah air mineral (50%, bb), jumlah CMC (500 mg/L), jumlah Na-Alginat (500 mg/L), jumlah asam sitrat (200 mg/L), dan jumlah asam askorbat (200 mg/L). Menggunakan piranti lunak Design Expert 13.0® dengan parameter desain model special cubic, algoritma pencarian both exchanges, dan jenis keoptimalan D-Optimality didapatkan 17 formulasi yang diukur respon fisik (Total Padatan Terlarut (TPT) dan Warna (L*, a*, b*, C*, h)), respon kimia (pH), dan respon sensori (warna, aroma, rasa, keseluruhan) untuk optimasi. Dari optimasi menggunakan respon 17 formulasi tersebut didapatkan formula optimal dengan komposisi 5% (bb) gula, 10% (bb) ekstrak wortel, 35% (bb) esktrak nanas, 50% (bb) air, 500 mg/L CMC, 500 mg/L Na-Alginat, 200 mg/L asam askorbat, dan 200 mg/L asam sitrat yang memiliki desirability 0,93. Pengukuran kapasitas antioksidan formula optimal menunjukkan bahwa formula optimal memiliki kapasitas antioksidan ekuivalen dengan 93,05 mg/L asam askorbat., The Indonesian soft drink market is currently saturated with the same kinds of drinks like RTD tea, soda, et cetera. Rarely do we find soft drinks based on fruit, and even rarer based on pineapple. This research is aimed to find an optimal formula for a soft drink based on pineapple-carrot juice using the Response Surface Method (RSM) using a D-Optimal mixture design. This research also aims to measure the antioxidant activity of the obtained optimal formula using the DPPH method. The formulation of the drink consists of three independent variable and five control variables, which are amount of carrot extract (10-30%, wb), amount of pineapple extract (15-35%, wb), and amount of sugar (5-10%, wb). The control variables are water (50%, wb), CMC (500 mg/L), Na-Alginate (500 mg/L), ascorbic acid (200 mg/L), and citric acid (200 mg/L). Formulation using Design Expert 13.0® with a special cubic model, both exchanges search algorithm using D-Optimality, we get a total of 17 formulas. These 17 formulas are then measured for physical response (Total soluble solids (TSS) and Color (L*, a*, b*, C*, h)), chemical response (pH), and sensory response (color, aroma, taste, overall). Using the responses from those 17 formulas, optimation was done to receive an optimal formula consisting of 5% (wb) sugar, 10% (wb) carrot extract, 35% (wb) pineapple extract, 50% (wb) water, 500 mg/L CMC, 500 mg/L Na-Alginate, 200 mg/L citric acid, and 200 mg/L ascorbic acid, which has a desirability of 0,93. Measuring the capacity of the optimal formula, it is found to be equivalent to 93.05 mg/L of ascorbic acid.
Keyword: Antioksidan, Optimasi Formula, Respon Sensori, Sari Buah

Judul: Ready to Drink Lemon Water
Formula Optimization using a D-Optimal Mixture Design
Abstrak: Meningkatnya permintaan terhadap minuman ready to drink (RTD) semakin mendorong industri makanan dan minuman untuk menciptakan formula optimal yang dapat memenuhi kebutuhan konsumen berdasarkan kualitas, umur simpan, manfaat, dan bahan baku yang digunakan. Penelitian ini bertujuan untuk menentukan formula optimal lemon water RTD menggunakan d-optimal mixture design dengan mempertimbangkan respon fisik dan sensori hedonik, kemudian menganalisis perbandingan kandungan antioksidan (DPPH) dan sensori hedonik antara formula optimal dengan produk komersil. Komposisi bahan dengan batas bawah-atas adalah sebagai berikut: sari lemon (5,00-15,00%), GKR (5,00-10,00%), HFS (2,00-5,00%), pewarna (0,00-0,25x10-2%), dan air (70,00-88,00%). Rancangan formula yang dihasilkan peranti lunak Design Expert 13.0® sebanyak 25 rancangan formula. Penentuan jumlah panelis pada uji sensori menggunakan metode balanced incomplete block design. Hasil penelitian menunjukkan formula optimal (5,00% sari lemon, 10,00% GKR, 5,00% HFS, 0,15x10-2% pewarna, dan 80,00% air) memiliki desirability sebesar 0,927. Formula optimal yang dihasilkan tidak memiliki kapasitas antioksidan namun memiliki tingkat penerimaan sensori tertinggi berdasarkan atribut warna, aroma, rasa, dan overall dibandingkan dengan dua produk komersil lainnya sehingga produk lemon water RTD dapat dikatakan layak dikembangkan menjadi produksi skala pilot plant., The increasing demand for ready to drink (RTD) drinks further encourages the food and beverage industry to create optimal formulas that can meet consumer needs based on quality, shelf life, benefits, and raw materials used. This study aims to determine the optimal formula of lemon water RTD using d-optimal mixture design by considering physical response and hedonic sensory, then analyzing the comparison of antioxidant content (DPPH) and hedonic sensory between the optimal formula and commercial products. The ingredient composition with lower and upper limits is as follows: lemon juice (5,00-15,00%), GKR (5,00-10,00%), HFS (2,00-5,00%), colorant (0,00-0,25x10-2%), and water (70,00-88,00%). The design formula produced by Design Expert 13.0® software was 25 design formulas. The determination of the number of panelists in the sensory test used the balanced incomplete block design method. The results showed that the optimal formula (5,00% lemon juice, 10,00% GKR, 5,00% HFS, 0,15x10-2% coloring, and 80,00% water) had a desirability of 0.927. The optimal formula produced does not have antioxidant capacity but has the highest level of sensory acceptance based on color, aroma, taste, and overall attributes compared to the other two commercial products so that RTD lemon water products can be said to be feasible to be developed into pilot plant scale production.
Keyword: Antioksidan, Sensori hedonik, Optimasi formula, lemon water RTD

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
Keyword: