# Linear Programming

Allstate Oil produces two grades of gasoline: reguler 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 contains 0.6 gallons of grade A crude oil.

For the next production period, Allstate has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasoline has a production capacity of 50,000 gallons for the next production period. Allstate distributors indicated that the demand for the premium gasoline for the next production period would be at most 20,000 gallons.

1) Formulate a linear programming model that can be used to 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.

2) Write the linear programming in standard form

3) What is the optimal solution

4) What are the values and interpretations of the slack variables

5) What are the binding constraints

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#### Solution Summary

Allstate Oil 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 contains 0.6 gallons of grade A crude oil.

For the next production period, Allstate has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasoline has a production capacity of 50,000 gallons for the next production period. Allstate distributors indicated that the demand for the premium gasoline for the next production period would be at most 20,000 gallons.

1) Formulate a linear programming model that can be used to 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.

2) Write the linear programming in standard form

3) What is the optimal solution

4) What are the values and interpretations of the slack variables

5) What are the binding constraints