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 used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. 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. If required, round your answers to two decimal places. Let R = number of gallons of regular gasoline produced P = number of gallons of premium gasoline produced fill in the blank 2 R + fill in the blank 3 P s.t. fill in the blank 4 R + fill in the blank 5 P fill in the blank 7 Grade A crude oil available fill in the blank 8 R + fill in the blank 9 P fill in the blank 11 Production capacity fill in the blank 12 P fill in the blank 14 Demand for premium R, P fill in the blank 16 What is the optimal solution? Gallons of regular gasoline fill in the blank 17 Gallons of premium gasoline fill in the blank 18 Total profit contribution $fill in the blank 19 What are the values and interpretations of the slack variables? Constraint Value of Slack Variable Interpretation 1 fill in the blank 20 2 fill in the blank 22 3 fill in the blank 24 What are the binding constraints? Grade A crude oil available Production capacity Demand for premium

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Problem 7-41

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 used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons.

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. If required, round your answers to two decimal places.

Let R	=	number of gallons of regular gasoline produced
P	=	number of gallons of premium gasoline produced

	fill in the blank 2 R	+	fill in the blank 3 P
s.t.
	fill in the blank 4 R	+	fill in the blank 5 P	fill in the blank 7	Grade A crude oil available
	fill in the blank 8 R	+	fill in the blank 9 P	fill in the blank 11	Production capacity
			fill in the blank 12 P	fill in the blank 14	Demand for premium
			R, P	fill in the blank 16

What is the optimal solution?

Gallons of regular gasoline fill in the blank 17

Gallons of premium gasoline fill in the blank 18

Total profit contribution $fill in the blank 19
What are the values and interpretations of the slack variables?

Constraint Value of Slack Variable
Interpretation

1 fill in the blank 20

2 fill in the blank 22

3 fill in the blank 24
What are the binding constraints?

Grade A crude oil available

Production capacity

Demand for premium