# Linear Programming

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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

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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