Raptor Fuels produces three grades of gasoline - Regular, Premium, and Super. All of these are produced by blending two types of crude oil - Crude A and Crude B. The two types of crude contain specific ingredients which help in determining the octane rating of gasoline. The important ingredients and the costs are contained in the following table:
CRUDE A
CRUDE B
Cost per gallon
$0.42
$0.47
Ingredient 1
40%
52%
Other ingredients
60%
48%
In order to achieve the desired octane ratings, at least 41% of Regular gasoline should be Ingredient 1; at least 44% of Premium gasoline must be Ingredient 1, and at least 48% of Super gasoline must be Ingredient 1. Due to current contract commitments, Raptor Fuels must produce at least 20,000 gallons of Regular, at least 15,000 gallons of Premium, and at least 10,000 gallons of Super.
a. Formulate a linear program that could be used to determine how much of Crude A and Crude B should be used in each of the gasoline to meet the demands at the minimum cost.
b. What is the minimum cost?
c. How much of Crude A and Crude B are used in each gallon of the different types of gasoline?