# Modelling the production plan of an oil company

How do I set up the problem and find the maximum profit? I have tried for hours but still confused.

Linear programming

The Grand Strand Oil Company

The Grand Strand Oil Company produces regular and premium gasoline for independent service stations in the southeastern United States. The Grand Strand refinery manufactures the gasoline products by blending three petroleum components. The gasoline is sold at different prices, and the petroleum components have different costs. The firm wants to determine how to mix or blend the three components into the two gasoline products and maximize profits.

The regular gasoline can be sold for $1.00 per gallon and premium gasoline for $1.08 per gallon. For the current production planning period, Grand Strand can obtain the three petroleum components at the cost per gallon and in the quantities shown in Table1.

Product specifications for the regular and premium gasoline restrict the amounts of each component that can be used in each gasoline product. Table 2 lists the product specifications. Current commitments to distributors require Grand Strand to produce at least 10,000 gallons of regular gasoline.

The Grand Strand blending problem is to determine how many gallons of each component should be used in the regular gasoline blend and how many should be used in the premium gasoline blend. The optimal blending solution should maximize the firm's profit, subject to the constraints on the available petroleum supplies shown in Table 1, the product specifications shown in Table 2, and the required 10,000 gallons of regular gasoline.

1) Formulate and solve linear programming model that maximize the firm's profit.

2) Write a brief report that explains your findings.

Table 1. Petroleum Cost and Supply for the Grand Strand Company

Petroleum Component Cost/Gallon Maximum Available

1 $0.50 5,000 gallons

2 $0.60 10,000 gallons

3 $0.84 10,000 gallons

Table 2. Product Specifications for the Grand Strand Company

Product Specifications

Regular gasoline

At most 30% component 1

At least 40% component 2

At most 20% component 3

Premium gasoline

At least 25% component 1

At most 40% component 2

At least 30% component 3

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#### Solution Preview

Dear my friend,

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#### Solution Summary

We aim to biuld up an linear programming formulation which maximizes the profit of an oil company according to some condition. We go throught the description of the problem and generate the correponding constraints aiming to maximize profit earned by the company. This will result in an LP. We will use GAMS software to solve the mode.