A refinery produces two grades of gasoline: regular and premium by blending two

Question

A refinery produces two grades of gasoline: regular and premium by blending two types of crude oil. Although the two types of crude contain the two important ingredients required to produce both gasoline,the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredient A and B in each type of crude oil and the cost per gallon are shown below. Crude 0il Cost Ingredient Ingredient B $0.10 20% 60% $0.15 50% 30% Each gallon of regular must contain at least 40% of A, whereas each gallon of premium can contain at most 50% of B. Daily demand for regular gasoline is 800,000 gallons and daily demand or premium gasoline is 500,000 gallons. Formulate and do not solve a linear programming model to determine how many gallons of each type of crude oil should be used to produce the required quantities of regular and premium gasoline to satisfy the daily demand at a minimum cost.

Explanation / Answer

X1 and X2 are the quantities of two types of crude oil 1 and 2 for producing regular.

Objective function is

Minimise 0.1X1 + 0.15X2

subject to

0.2x1+0.5x2 =>0.4 ( X1+X2)

X1+x2= 80000

Or 0.2X1+0.5X2 =>32000 ---- condition 1

Let x3 and x4 are the quantities of crude 1 and 2 respectively to produce premier gasoline.

Minimise 0.1X3+0.15X4

Subject to

X3+X4 = 50000

0.6 X3+ 0.3X4 <=0.5 (X3+X4) or 0.6X3+0.3X4 <= 25000. ----- condition 2

Combined objective function

Minimise 0.1(X1+X3)+0.15( X2+X4)

Subject to conditions 1 and 2.

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