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. Ea

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.

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. 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

2. 	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

4. 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

6. What are the values and interpretations of the slack variables?

   Constraint	Value of Slack Variable	Interpretation
   	fill in the blank 20
   	fill in the blank 22
   	fill in the blank 24

8. What are the binding constraints?

Binding or not binding?