Question: Help solving a linear programming question. Here is the question: Energy Oil Company is a gasoline refiner and wholesaler. It sells two products to gas

Help solving a linear programming question. Here is the question:

Energy Oil Company is a gasoline refiner and wholesaler. It sells two products to gas stations: regular and premium gasoline. It makes these two final products by blending together four raw gasolines and some chemical additives (the amount and cost of the additives per barrel are assumed to be independent of the mixture). Each gasoline has an octane rating that reflects its energy content. In the United States, it is required that gas pump label the correct octane level. Nearly all states do regular testing to make sure gas stations are in compliance. Table 1 lists the octane, purchase price per barrel, and availability at that price per day. This table also gives the required minimum octane for each final gasoline, the net selling price per barrel (removing the cost of the additives), and the expected daily demand for gas at that price.

Table 1: Energy Oil Data

Raw gasoline

octane Cost ($/b)

Available

daily

1 86 17 20,000
2 88 18 15,000
3 92 20.5 15,000
4 96 23 10,000
Products Selling price Max daily demand
regular 89 19.5 35,000
premium 93 22 23,000

(This is the question to solve)

Can you formulate the constraint on Octane now?

Provided note below to assist:

Octane of regular = [86 * (barrels of raw gas 1 used/day to make regular) + 88 * (barrels of raw gas 2 used/day to make regular) + ...+ 96 * (barrels of raw gas 4 used/day to make regular)], divided by the [total barrels of raw gases blended into regular gasoline], which should be at least 89.

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