# Linear Programming: Examining an Oil Company

Linear Programming Question:

A Southern Oil Company produces two grades of gasoline; Regular and Premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery that used to produce the gasoline has a production capacity if 50,000 gallons for the next production period. Southern Oils distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

A) Determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. Let R= number of gallons of regular gasoline produced Let P = number of gallons of premium gasoline produced.

B)What is the optimal solution?

- Gallons of regular gasoline

- Gallons of premium gasoline

- Total profit contribution

C) What are the values and interpretations of the slack variables?

D) What are the binding constraints?

- Grade A crude oil available

- Production capacity

- Production capacity

#### Solution Preview

The first thing to do here is to specify the variables for the linear programming question. This is actually specified in part A of the question since what is requested is the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize total profit contribution. Therefore we have two variables:

R = number of gallons of regular gasoline produced

P = number of gallons of premium gasoline produced

We then break up the question into parts to see all the values that will be needed to solve the question:

The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline.

This means that each gallon of regular gasoline produced will make a ...

#### Solution Summary

A four page long step by step explanation, using graphs, of a linear programming formulation and subsequent graphical method calculation of the optimal solution finding also any slack variables and therefore determining any binding constraints.