Bharat Rasayan Limited (BRL) uses a crude oil derivative, called HC and produces 3 products. HC is mixed with additive A using a chemical process to give Regular grade lubricant, RG. Some portion of the RG can be used as it is, and the remaining can be mixed with additive B to produce Premium grade lubricant (PG). Some portion of the PG can be used as it is and the remaining can be mixed with additive C to produce Super Premium grade lubricant (SP). The ratio in which each set of inputs is mixed to produce the product is not fixed precisely, but the quantity of each additive used should be at least 40% and at most 50% of the other input. For instance, additive A should be between 40% and 50% of HC used for producing RG. RG PG SP Cost (processing + all raw material) Rs per barrel 5400 6600 7700 Minimum Demand (barrels) 1,000,000 800,000 600,000 BRL has sufficient quantities of HC and the additives in stock. But they want to ensure that no SP is held in inventory after production, i.e. the finishing stock of SP should be zero. The cost of HC is Rs.6000 per barrel. Formulate a suitable Mathematical Program to help BRL. [6 marks]
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