Question

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. Max	R	+	P
   s.t.
   	R	+	P	≤		Grade A crude oil available
   	R	+	P	≤		Production capacity
   			P	≤		Demand for premium
   			R, P

3. What is the optimal solution?
   

   Gallons of regular gasoline
   Gallons of premium gasoline
   Total profit contribution	$

Answer 1

Answer:

a)

Decision variables:

Let

R = number of gallons of regular gasoline produced

P = number of gallons of premium gasoline produced

Objective function is to maximize profits

Max Z = 0.3R + 0.5P

Constraints:

0.3R + 0.6P <= 18000

R+P<= 50000

P<=20000

R,P>=0

b)

Optimal Solution:

40,000 gallons of regular gasoline

10,000 gallons of premium gasoline

Total profit contribution = $17,000

THANKYOU!