Application of Linear Programming to Optimize Soap Production Using Oil from Irvingia Gabonensis (Ogbono) Seed

Abstract

The efficiency of a soap produced with oil extracted from obgono (irvingia gabonensis) seed using Operational Research (linear programming) was investigated. Oil was first extracted from two (2) grounded sizes (1.4mm and 1.0mm) of ogbono seed using a soxhlet set-up and hexane as solvent. 47.98% and 43.64% of oil were extracted from 1.0mm and 1.4mm sizes respectively. This means that more oil was extracted from smaller grounded size. Four (4) pastes of soap were produced with 25ml each of 2 molar and 1 molar concentration of Sodium Hydroxide (NaOH) in four different mass of the extracted oil. 1 molar concentration of NaOH averagely produced more mass (15.5g) of soap than the 2 molar concentrations which averagely produced 8.25g of soap. The parameters used to produce the soap were optimised. Caustic soda (NaOH) was maximized being the objective function of the optimization model and it gave a value of 3.98 unit for every 1.99 unit of paste 1. The unused constrains value (rate of reaction of reagent i.e time and oil) for the production were 242.4 capacity and 0.2 capacity which at this point no further iteration can be done because the objective row in the last tableau table has no negative value.