OILCO produces three grades of gasoline (regular, premium, and super) by blending three types of crude oil. All three types of crude oil contain two important ingredients (X and Y) required to produce the three gasoline grades.

The percentage of the ingredients differs in each type of crude oil. These percentages are given in the following table:

Crude oil type

1 2 3
Ingredient X 40 20 55
Ingredient Y 35 30 60

Cost of each type of crude oil is $0.80, $0.60, and $0.40 per gallon for crude oil types 1, 2, and 3 respectively. Each gallon of regular gasoline must contain at least 35% of ingredient X. Each gallon of premium gasoline can contain at most 45% of ingredient Y. Each gallon of super gasoline can contain at most 40% of ingredient Y. Daily demand for regular, premium, and super grades of gasoline is 400,000, 150,000, and 150,000 gallons, respectively. Daily production quantities are 350,000 gallons for crude oil

1; 250,000 gallons for crude oil

2; and 200,000 for crude oil

3. How many gallons of each type of crude oil should be used in the three grades of gasoline to satisfy demand at minimum cost?

Required:

(i) Formulate a linear programming model for the above problem

(ii) Solve the model using spreadsheet and interpret results. (20 marks)