A Mathematical model on the production mix of plants in the redberrytree farm / by Ella Gean B. Avila and Abegail Jean M. Tangara.

Thesis (Bachelor of Science in Industrial Engineering) Cavite State University

College of Engineering and Information Technology (CEIT)

AVILA, ELLA GEAN B. and TANGARA, ABEGAIL JEAN M. A Mathematical Model on the Production Mix of Plants in the Redberry tree Farm. Undergraduate Thesis. Bachelor of Science in Industrial Engineering. Cavite State University, Indang, Cavite. June 2022. Adviser: Ms. Mary Joyce P. Alcazar.

The study was conducted with the aim of constructing a mathematical model to determine the optimal plant product mix for Redberry tree Farm, a small-scale farm in Dasmariñas, Cavite. Specifically, this study aimed to: (1) identify the main problem/s of the farm; (2) gather the data needed to construct a mathematical model; (3) identify the methods needed in constructing a mathematical model; (4) formulate a mathematical model; (5) verify the formulated mathematical model using various methods; and (6) provide feasible recommendations. The Define, Measure, Analyze, Design, and Verify (DMADV) methodology was used to achieve the study's objectives. In the study's methodology, the main problem was identified in the Define Phase, which is the farm's low-profit yield. A cause-and-effect diagram was utilized, and results indicated that the major cause was improper resource allocation, caused by the unutilized 8,000 square meters land area. Data were gathered through interviews with the owner and farmworker using a semi-structured questionnaire. The data focused on the selected main crops: guyabano, papaya, mango, rambutan, banana, and avocado. In the Measure Phase, additional data regarding resource allocation used in the mathematical model were presented. During the Analyze Phase, data gathered were categorized into sets, scalars, and parameters. Then, these summarized data were used to formulate the mathematical model using the General Algebraic Modeling System (GAMS) software during the Design Phase. The first optimal solution resulted in an annual profit of Php 356,602 obtained from the crop quantity of 98 mango trees, one worker, seven man-hours of labor used, and 4,836 square meters of utilized land. Five alternative options were presented during the Verify Phase to calculate optimal alternative results. There was a total of four optimal alternative results obtained. Option 4 got the highest annual profit of Php 482,937 resulting from the crop mix of 146 mango trees and 33 avocado trees, two workers with seven man-hours each of labor used, and 8,000 square meters of utilized land. Furthermore, the study recommended using the mathematical model using the data from option 4 to increase the profit yield of the farm.

Submitted copy to the University Library. 08/03/2022 T-9155