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.

LetR=number of gallons of regular gasoline producedP=number of gallons of premium gasoline produced

Max

fill in the blank 2

R+fill in the blank 3

Ps.t.fill in the blank 4

R+fill in the blank 5

P

fill in the blank 7

Grade A crude oil availablefill in the blank 8

R+fill in the blank 9

P

fill in the blank 11

Production capacityfill in the blank 12

P

fill in the blank 14

Demand for premiumR,P

fill in the blank 16

What is the optimal solution?

Gallons of regular gasolinefill in the blank 17

Gallons of premium gasolinefill in the blank 18

Total profit contribution$fill in the blank 19

What are the values and interpretations of the slack variables?

ConstraintValue of Slack Variable

Interpretation1fill in the blank 20

2fill in the blank 22

3fill in the blank 24

What are the binding constraints?

Grade A crude oil available

Production capacity

Demand for premium